He will announce his bid by video on Thursday, Reuters reports, citing “a source familiar with the plans”.
He is then expected to make his first public appearance as a candidate next week at an event in Pittsburgh featuring union members, a key constituency.
Mr Biden enters a crowded Democrat field all hoping to take on Mr Trump in 2020.
His move comes after months of speculation as to whether he’d run or not. He will take on 20 other hopefuls, but for now he leads the pack, opinion polls show.
His candidacy will face numerous questions, including whether he is too old and too centrist for a Democratic Party increasingly propelled by its more vocal liberal wing.
Furthermore, questions have arisen about his propensity for touching and kissing strangers at political events, with several women coming forward in recent weeks to say he had made them feel uncomfortable.
Mr Biden struggled in his response to the concerns, at times joking about his behaviour. He eventually apologised and said he recognised standards for personal conduct had evolved in the wake of the #MeToo movement.
Many believe the 76-year-old is also offering US voters experience and the promise of exposing the scandals and chicanery of Mr Trump’s administration.
In the US, commentators have said among the US’s working population, Mr Biden’s experience and dignity could be the antidote to Mr Trump’s angry outbursts.
“We can’t be divided by race, religion, by tribe,” he Biden said last month.
“In America, everybody gets a shot.”
Despite failing to win over Democrats in his previous attempts to secure the nomination in 1988 and 1998, Mr Biden is in a strong position in national polls and early voting states. He will run as a centrist Obama-Biden Democrat anchored by strong union support.
He will reportedly attack Mr Trump as a populist and a friend of Wall Street bosses who hit the jackpot with US tax laws.
In a speech to union members in April, Mr Biden called Mr Trump a “tragedy in two acts.”
“This country can’t afford more years of a president looking to settle personal scores,” he said.
Mr Biden’s candidacy will offer early hints about whether Democrats are more interested in finding a centrist who can win over the white working-class voters who went for Trump in 2016, or someone who can fire up the party’s diverse progressive wing, such as Senators Kamala Harris of California, Bernie Sanders of Vermont or Elizabeth Warren of Massachusetts.
Additional reporting by Reuters