The president said the federal agency overseeing the handover must “do what needs to be done”, even as he vowed to keep contesting his election defeat.
The General Services Administration (GSA) said it was acknowledging Mr Biden as the “apparent winner”.
It came as Mr Biden’s victory in the state of Michigan was officially certified, a major blow to Mr Trump.
The GSA announcement means the president-elect now has access to top security briefings, office space and government officials as he prepares to take office on 20 January.
His transition website has now changed to a US government domain. He will begin announcing the people he wants in the top jobs in his cabinet on Tuesday.
Has Trump conceded?
Mr Trump tweeted as the GSA, which is tasked with formally beginning presidential changeovers, informed the Biden camp that it would start the transition process.
GSA administrator Emily Murphy said she was making $6.3m (£4.7m) in funds available to the president-elect.
Mr Trump said: “In the best interest of our Country, I am recommending that Emily and her team do what needs to be done with regard to initial protocols, and have told my team to do the same.”
He did not concede, however, and went on to repeat unsubstantiated claims of corruption, pledging to keep up the “good fight”. It is worth noting that Mr Trump does not have to concede for Mr Biden to be sworn in as the 46th US president.
Ms Murphy, a Trump appointee, cited “recent developments involving legal challenges and certifications of election results” in her decision to start the transition process.
She said she had received no pressure from the White House over the timing of the move.
“I did, however, receive threats online, by phone, and by mail directed at my safety, my family, my staff, and even my pets in an effort to coerce me into making this determination prematurely,” Ms Murphy said in a letter to Mr Biden.
“Even in the face of thousands of threats I have remained committed to upholding the law.”
She had faced criticism from both political sides for failing to begin the transition process sooner, usually a routine step between the election and the inauguration.