Trump, and other Republican ’24 contenders, push claims of injustice.

Mr. Weiss was given the authority over whether to bring charges; Merrick B. Garland, the attorney general, had offered assurances that Mr. Weiss would be free to run the investigation.

He worked in the Delaware U.S. attorney’s office during the Bush and Obama administrations before Mr. Trump appointed him to lead it. He graduated from Washington University in St. Louis and Widener University School of Law, and is a member of the Delaware and Pennsylvania bars.

Both Democrats and Republicans approved of his nomination in 2017.

“David is a career prosecutor and dedicated public servant, longtime Delawarean, and valued member of our law enforcement community,” Senator Chris Coons, Democrat of Delaware, said in a statement, according to The News-Journal.

Announcing Mr. Weiss’ nomination, Mr. Trump said in a statement in 2017 that he would “share the president’s vision for ‘Making America Safe Again.’”

The crimes to which Mr. Biden is pleading guilty, Mr. Berman said, are ones that the average person is rarely prosecuted for because they are usually only brought along with more serious offenses.

In Mr. Biden’s case, they include a charge stemming from lying about drug use on the government form used for his purchase of a handgun. Current and former officials say tens of thousands of Americans, out of the 25 million who buy guns each year, lie on their forms and are not prosecuted.

Prosecutors had pored over Mr. Biden’s finances, including examining two years of unpaid taxes. But in 2021, Mr. Biden paid the I.R.S. the full amount that his accountants estimated he owed, and paid off his liens.

By making the payments, former officials said, Mr. Biden complicated the ability of prosecutors to charge him with tax evasion because juries often question why the government has indicted someone who has paid his taxes. That left prosecutors with the options to charge Mr. Biden with filing his 2017 and 2018 taxes late — something that Mr. Biden’s lawyers argued to prosecutors are often handled without criminal charges and that in this case were handled as misdemeanors.

“If these are the only offenses, most prosecutors are going to say it’s not worth a federal case — they would say: Let’s not make a federal case of it for the average person because it’s not worth it to bring a case unless there’s reason to be concerned that there’s a public safety issue or the trust that everyone is treated equally under the law is at stake,” Mr. Berman said.

Mr. Berman said that in this case, federal prosecutors are in a unique situation because there was a very high-profile defendant who was the subject of investigations for a range of activities. The failure to bring some charges when there is no factual dispute, he said, could create the impression of a two-tiered system of justice.

“Everyone is paying attention and the facts are not in dispute, so a failure to bring charges would create the perception that there was some sort of special treatment or leniency being given to the president’s son,” Mr. Berman.

Mr. Trump dismissed the plea deal as a slap on the wrist.

“The corrupt Biden DOJ just cleared up hundreds of years of criminal liability by giving Hunter Biden a mere ‘traffic ticket,’” Mr. Trump proclaimed on his website, Truth Social. “Our system is BROKEN!”

And Mr. DeSantis wrote on Twitter, “If Hunter was not connected to the elite D.C. class he would have been put in jail a long time ago.”

Republicans argued that the plea agreement, in which President Biden’s son pleaded guilty to two misdemeanor tax charges with no jail time, in no way evened the scales of justice.

“The Hunter Biden plea deal is a joke,” said Vivek Ramaswamy, the entrepreneur-turned-presidential candidate who, among those in the G.O.P. field not named Trump, has most fully embraced the idea that Mr. Trump’s indictment in a case involving his handling of classified documents was purely political. “It’s a feigned retreat and reveals they’re even more scared than ever of scrutiny for the real crimes.”

Even one of Mr. Trump’s biggest critics on the Republican primary campaign trail, former Gov. Asa Hutchinson of Arkansas, was hardly putting the matter to rest, bringing up unsubstantiated allegations of bribery that party leaders in the House are pushing hard.

“It is important for our country to have the whistle blower allegations answered, and the U.S. attorney and the Department of Justice should be transparent in stating clearly the status of the investigation; the reason for a 5 year delay in reaching today’s result; and how the investigation will continue and who is leading it?” Mr. Hutchinson said.

Mr. Hutchinson said that if the plea deal closed the books on the earliest charges against Hunter Biden, a new special counsel needs to be named to investigate the latest charges that emerged from the efforts by Rudolph W. Giuliani to dig up dirt on the president in Ukraine.

Democrats unsurprisingly praised the Justice Department’s action as proof positive that unlike the Trump administration, the Biden administration is playing it straight with prosecutions that carry political potency.

“This episode just underscores the integrity of President Biden — he kept Trump’s U.S. attorney on to investigate a matter involving his own son,” read a statement by Facts First USA, a pro-Biden organization backed by organized labor. The group’s president, David Brock, added, “It’s time for Republicans to put this shameless inquisition to bed — America is exhausted by their stunts and ready for them to govern like adults.”

After his father became vice president, Hunter Biden, a Yale-educated lawyer, forged business relationships with foreign interests that brought him millions of dollars, raised questions about whether he was cashing in on his family name, set off alarms among government officials about potential conflicts of interest, and provided Republicans an opening for years of attacks on his father.

And after the death of his brother, Beau, in 2015, Hunter descended into a spiral of addiction and tawdry and self-destructive behavior.

He is sober now and no longer entangled in foreign business deals. He is a visible presence in his father’s life — his oldest daughter was married at the White House in November, and he attended a state dinner last month.

An examination by The New York Times of the investigation and Hunter Biden’s journey to this juncture, based on interviews with his former business partners, family members and close friends, as well as officials and lawyers familiar with the Justice Department investigation, does not provide either side with the narrative they would prefer.

What emerges is the story of a man battling with personal demons against the background of family tragedy and under the glare of public scrutiny. It is an instructive look at the enduring Washington practice of trading on access and influence.

The Justice Department would charge Mr. Biden but agree not to prosecute him in connection with his purchase of a handgun in 2018 during a period when he was using drugs. The deal would be contingent on Mr. Biden remaining drug free for 24 months and agreeing never to own a firearm again.

The agreement must still be approved by a federal judge. Mr. Biden is expected to appear in federal court in Delaware in the coming days to be arraigned on the misdemeanor tax charges and plead guilty.

“With the announcement of two agreements between my client, Hunter Biden, and the United States Attorney’s Office for the District of Delaware, it is my understanding that the five-year investigation into Hunter is resolved,” Mr. Biden’s lawyer, Christopher Clark, said in a statement.

A White House spokesman, Ian Sams, said in a statement, “The president and first lady love their son and support him as he continues to rebuild his life. We will have no further comment.”

Assuming there are no last-minute changes or complications, the deal would most likely resolve the investigation without Mr. Biden facing a federal prison sentence.

But it would by no means end the superheated politics of the case. Republicans have sought for years to make the case that Hunter Biden committed an array of crimes that should put him behind bars and call into question the honesty of his father.

Coming less than two weeks after the Justice Department indicted former President Donald J. Trump on charges that he risked exposing national security secrets and obstructed efforts by the government to reclaim classified documents from him, an agreement that allows Hunter Biden to walk free is also sure to bring a torrent of criticism from the right and intensified efforts by House Republicans to portray the Justice Department and the F.B.I. as biased.

As president, Mr. Trump had long sought to tie Hunter Biden’s business deals and personal troubles to his father. Mr. Trump’s first impeachment had its roots in his efforts to persuade the Ukrainian government to help him show wrongdoing in Hunter Biden’s work for Burisma, a Ukrainian energy company, and while in the White House he pressured the Justice Department to investigate.

The Justice Department investigation continued after President Biden took office, under the oversight of the U.S. attorney for Delaware, David C. Weiss, a Trump appointee who was kept on to allow him to finish the inquiry. Attorney General Merrick B. Garland has testified to Congress that Mr. Weiss had full authority and independence to decide whether to bring a case against Mr. Biden.

Along with resolving the main legal issues confronting Hunter Biden, the agreement is a victory for his lead lawyer, Mr. Clark, a hard-charging former federal prosecutor. In meetings with Justice Department officials over the past year and a half, he has presented them with evidence intended to convince them that any prosecution of his client would be weak.

“Hunter will take responsibility for two instances of misdemeanor failure to file tax payments when due pursuant to a plea agreement,” Mr. Clark said in his statement. “A firearm charge, which will be subject to a pretrial diversion agreement and will not be the subject of the plea agreement, will also be filed by the government. I know Hunter believes it is important to take responsibility for these mistakes he made during a period of turmoil and addiction in his life. He looks forward to continuing his recovery and moving forward.”

The investigation focused on a particularly chaotic and unseemly period in Hunter Biden’s life when he was addicted to crack cocaine. But the Justice Department went through nearly every major aspect of his life over the past 15 years — a period in which he also struggled to control his alcoholism and engaged in international business deals, which he got into at least in part because of his father’s prominence in politics.

And despite federal investigators casting their nets wide — including examining Mr. Biden’s work for Burisma and his business dealings with an energy tycoon in China — the investigation ultimately narrowed to two separate issues.

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One was his taxes. Prosecutors had been weighing whether to indict him in connection with his failure to meet filing deadlines for his 2017 and 2018 taxes, and whether he had improperly claimed $30,000 in deductions for business expenses.

The second was whether he lied on a United States government form that he filled out when he purchased the handgun in 2018. In response to a question on the form about whether he was using drugs, Mr. Biden had said he was not — an assertion that prosecutors suspected might be false based on his erratic behavior at the time and accounts from people who interacted with him.

Those charges were far less explosive than ones pushed by Mr. Trump and congressional Republicans, who have been angry with the Justice Department for failing to find wider criminal wrongdoing by the president’s son and family.

Since taking control of the House in January, top Republicans have used their new investigative power to push the narrative that the president has been complicit in an effort engineered by his son to enrich his family by profiting from their positions of power.

No one questions that Mr. Biden, a 53-year-old Yale-educated lawyer, has had significant personal troubles and pursued a professional path that has intersected with his father’s in ways that raised ethical issues.

After his father became vice president, he built relationships with wealthy foreigners that brought in millions of dollars, surfacing concerns inside the Obama administration and among government watchdog groups that he was cashing in on his family name.

He went into a downward spiral after his brother, Beau, died in 2015, becoming addicted to crack and engaging in tawdry, self-destructive behavior.

But the questions about what occurred during that period never led to conduct that prosecutors believed could win them a conviction in court.

In Ukraine, Hunter Biden sat on the board of Burisma, which was led by an oligarch who at the time was under investigation for corruption. He was paid tens of thousands of dollars a months for the position, which he held while his father was vice president and overseeing the Obama administration’s Ukraine policy.

Republicans have also pointed to an equity stake that Hunter Biden took in a Chinese business venture, and to his failed joint venture with a Chinese tycoon who had courted well-connected Americans in both major parties — at one point he gave the younger Mr. Biden a large diamond as a gift — but who was later detained by Chinese authorities.

Allegations promoted by Republicans that the elder Mr. Biden’s Justice Department went easy on his son are unlikely to fade away.

In April, an I.R.S. supervisor who had been overseeing the investigation into Hunter Biden hired a lawyer and went to Congress, alleging political favoritism in how the investigation had been handled. Congressional Republicans have pledged to investigate the claims, which have also been referred to inspectors general at the Justice Department and I.R.S.

Seamus Hughes contributed reporting.