Shortly after the decision was revealed, Donald Trump tweeted that he had approved the move, but said his disputed fraud case 'strongly continues'.
The government body that oversees US presidential transitions has informed Joe Biden that the process can formally begin.
A letter from US General Services Administration head Emily Murphy to Mr Biden on Monday said he would now have access to resources that had been denied to him because of the legal challenges seeking to overturn his win.
Ms Murphy said she had not been pressured by the White House to delay the formal transition and she did not make her decision "out of fear or favouritism".
"Please know that I came to my decision independently, based on the law and available facts," she wrote.
"I was never directly or indirectly pressured by any Executive Branch official - including those who work at the White House or GSA - with regard to the substance or timing of my decision. To be clear, I did not receive any direction to delay my determination."
Ms Murphy said she had received threats online, by phone and by mail directed at her, her family and her pets to try and get her to make her decision earlier.
"Even in the face of thousands of threats, I always remained committed to upholding the law," she wrote.
Shortly after the decision was revealed, Mr Trump tweeted that he had approved the move, but also said his disputed fraud case "STRONGLY continues".
Biden reveals key cabinet picks
Mr Biden on Monday named the deeply experienced Antony Blinken for secretary of state, also nominating the first female head of intelligence and a czar for climate issues, with a promise to a return to expertise after the turbulent years of Mr Trump.
As Mr Trump continued to make flailing attempts at overturning the results of the election three weeks ago, Mr Biden's rollout of cabinet names was his biggest step yet to signalling he is ready to take over on 20 January.
The list put out by Mr Biden's team ahead of a formal announcement Tuesday demonstrated a push to lower the temperature in Washington and restore traditional US leadership abroad.
"We have no time to lose when it comes to our national security and foreign policy," Mr Biden said in a statement.
"These individuals are equally as experienced and crisis-tested as they are innovative and imaginative."
Mr Blinken, a former number two of the State Department and a long-time advisor, will spearhead a fast-paced dismantling of Mr Trump's disruptive "America first" policies, including re-joining the Paris climate agreement and the World Health Organisation and resurrecting the Iran nuclear deal.
Mr Biden named the first woman, Avril Haines, as director of national intelligence, and the first Latino, Alejandro Mayorkas, to head the Department of Homeland Security, whose policing of tough immigration restrictions under Mr Trump was a frequent source of controversy.
Signalling the Democratic president-elect's campaign promise to raise the profile of global warming threats, he named former secretary of state John Kerry as a new special envoy on climate issues.
And in a further message of US re-engagement with the international community, Mr Biden named career diplomat Linda Thomas-Greenfield for UN ambassador. Jake Sullivan, who advised Biden when he was vice president under Barack Obama, was named national security advisor.
The picks underline an emphasis on professionals whom Mr Biden already knows well, in contrast to the Trump White House where officials were often picked without having traditional background for the job or proved incompatible and departed in acrimony.
The announcements come against an unprecedented backdrop of Mr Trump refusing to concede defeat and blocking Biden's access to the normal process for preparing an incoming government.
So far only a slowly growing minority of Republican leaders has denounced Mr Trump's conspiracy theory that mass fraud robbed him of victory, despite there being no evidence for this.
Many of Mr Biden's cabinet picks will require confirmation in the Senate, where Republicans hold a narrow majority, although this would change if Democrats score an upset victory in two Georgia Senate runoff elections.
Mr Trump remains defiant in spite of repeated failures by his legal team to prove their allegations in court.
The president, meanwhile, has largely halted at least his public work duties, while heading out to a golf course he owns in Virginia half a dozen times since the election.
On Monday, the White House once more announced that Mr Trump had no public events scheduled.
He has also not taken questions from reporters since the election - a previously unimaginable silence from a president who for most of his time in office sparred near daily with the press.
His options, however, are dwindling rapidly.
With Mr Biden having won a comfortable victory, Mr Trump is seeking to disrupt the normally routine process of state-by-state certification of results, followed by the formal December 14 vote by the Electoral College.
His campaign's latest focus is on seeking a two-week delay to certification of results in Michigan, which Mr Biden won by 155,000 votes on 3 November.
A Michigan state board was set to meet on the issue Monday.
Pennsylvania, another crucial state in Mr Biden's win, was expected to issue its certification after a federal judge threw out the latest baseless Mr Trump challenge on Saturday.
More cracks appeared in the facade of Republican unity over the weekend with Mr Trump confidant and former New Jersey governor Chris Christie calling the president's legal team a "national embarrassment."
Senator Patrick Toomey, from Pennsylvania, said after the court ruling there that Mr Trump had "exhausted all plausible legal options."
And on Monday, Senator Rob Portman, another Republican, said it was "time to expeditiously resolve any outstanding questions and move forward."
"There is no more sacred constitutional process in our great democracy than the orderly transfer of power after a presidential election," he wrote in The Enquirer newspaper.
There was also a push from Mr Trump's highest profile Wall Street backer, Stephen Schwarzman, who heads the Blackstone private equity group, who told Axios "the country should move on".