The US Attorney in Delaware has filed papers indicating a plea agreement has been reached.
He is expected to agree to drug treatment and monitoring.
The terms of the agreement are likely to keep him out of jail.
In theory, he still faces a maximum penalty of a year in prison on each of the tax charges and 10 years in prison on the gun charge, the justice department said in a statement. The proposed deal would need to be approved by the judge in the case, who will also determine the sentence.
It is unclear when Hunter Biden will appear in court to enter his guilty plea on the tax charges.
He will admit to felony gun possession as part of a “pre-trial diversion agreement” that is separate from the plea deal, his lawyer Chris Clark said in a statement.
“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,” Mr Clark added. “He looks forward to continuing his recovery and moving forward.”
Mr Clark told MSNBC that the conditions of his client’s probation were “up to to the court” but that he expected Mr Biden would be released without conditions after his court appearance.
“I think the judge is going to do what’s fair and I think what’s fair is my client gets on with his life,” he said.
Hunter Biden, 53, has previously worked as a lawyer, and a lobbyist including abroad in China and Ukraine. He was discharged from the US Navy in 2014 after testing positive for cocaine.
The plea deal brings to an end a long-running justice department investigation into whether he properly reported his income and made false statements on paperwork used to purchase a firearm in 2018.
The two misdemeanour tax charges stem from a failure to pay more than $100,000 (£78,000) in taxes in both 2017 and 2018. A former justice department official told CBS, the BBC’s US partner, that these amounts would lead to most clients being charged with misdemeanours, but “in the jail time range”.
The gun charge stems from a 2018 possession of a firearm while a drug user.
In a 2021 book, the younger Mr Biden admitted to being a heavy user of crack cocaine at that time.
But he reportedly said “no” on a federal form asking if he was “an unlawful user of, or addicted to, marijuana or any depressant, stimulant, narcotic drug or any other controlled substance”. Lying on these forms can lead to jail time.
The deal comes as some Republican lawmakers and presidential candidates have accused Joe Biden of “weaponising” the justice department against political opponents.
Hunter Biden has long been a target of scrutiny from conservatives, who have alleged that his dealings overseas indicate a pattern of corruption.
News of the plea deal was met with swift and strong criticism from Donald Trump and his campaign, as well as senior congressional Republicans.
Karoline Leavitt, a spokeswoman for the pro-Trump Make America Great Again Inc, called the agreement a “sweetheart deal” that allows the justice department to “turn a blind eye” to corruption. Mr Trump, for his part, called the deal a “mere traffic ticket”.
House majority leader Kevin McCarthy told reporters on Capitol Hill that the deal was evidence of a “two-tier” system of justice and vowed that the case would “enhance” a separate Republican investigation into Hunter Biden.
Prominent Democrats have remained largely quiet on the case. David Brock, a former right-wing investigative reporter turned pro-Democrat operative, said in a statement that the case should now be considered closed since “Hunter will not be charged with any of the unfounded and outlandish issues Republicans and right-wing media have used to smear him with for years”.
In a brief statement, the White House also said that Joe Biden and First Lady Jill Biden “love their son and support him as he continues to rebuild his life. We will have no further comment”.
While the younger Mr Biden has detailed a troubled life and “massive drug addiction”, he long denied engaging in illegal activity.
He first admitted knowledge of an investigation into him in December 2020.
In a statement at the time, he said that he was “confident that a professional and objective review of these matters will demonstrate that I handled my affairs legally and appropriately, with the benefit of professional tax advisers”.
Mr Clark has said he believes the investigation is now “resolved”, but the justice department in its statement said that the probe is “ongoing”.
