Trump, a Republican, has alleged widespread voter fraud in the November 3 election without providing evidence. Although he has not acknowledged Biden's victory, his announcement on Monday was the closest he has come to admitting defeat.
The General Services Administration, which is the federal agency that must sign off on presidential transitions, told Biden on Monday he could formally begin the handover process.
GSA Administrator Emily Murphy said in a letter that Biden would now have access to resources that had been denied to him because of the legal challenges seeking to overturn his win.
That announcement came shortly after Michigan officials certified Biden as the victor in their state, making Trump's legal efforts to change the election outcome even more unlikely to succeed.
Trump and his advisers said he would continue to pursue legal avenues but his tweet served as a sign that even the White House understood it was getting close to time to move on.
"Our case STRONGLY continues, we will keep up the good ... fight, and I believe we will prevail! Nevertheless, 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," Trump said in a tweet.
A statement by the Biden transition said meetings would begin with federal officials on Washington's response to the coronavirus pandemic, along with discussions of national security issues.
The move by the GSA means Biden's team will now have federal funds and an official office to conduct his transition until he takes office on January 20.
It also paves the way for Biden and Vice-President-elect Kamala Harris to receive regular national security briefings that Trump also gets.
Two Trump administration officials told Reuters the Biden agency review teams could begin interacting with Trump agency officials as soon as Tuesday.
Electors in each state will convene as the electoral college on December 14 to formally select the next president. Biden won 306 electoral votes, 36 over the 270 threshold needed to win.
Earlier on Monday, Biden named the top members of his foreign policy team, tapping trusted aide Antony Blinken to head the State Department and former US senator, secretary of state and 2004 Democratic presidential nominee John Kerry to serve as his special climate envoy.
Biden, who has said he would undo Trump's "America First" policies, also named Jake Sullivan as his national security adviser and Linda Thomas-Greenfield as US ambassador to the United Nations - both with high-level government experience.
He also is likely to tap former Federal Reserve chair Janet Yellen to become the next treasury secretary.
While Blinken, 58, has held important foreign policy positions in the past two Democratic administrations, including a spell as a deputy secretary of state under president Barack Obama.
Along with Sullivan, who was a deputy assistant to Obama and senior policy adviser to Hillary Clinton's 2016 presidential campaign, Blinken has helped Biden formulate a strategy that will include quick outreach to allies who have often been antagonised by Trump, and to demonstrate a willingness to work together on big global problems such as the coronavirus pandemic.
Biden has pledged to rejoin a nuclear deal with Iran if Tehran restores its compliance, return to the Paris climate accord and abandon plans to leave the World Health Organisation. Each move would reverse Trump's policies and some could take place quickly after the inauguration.
Biden took a step toward reversing Trump's hard-line immigration policies by naming Cuban-born lawyer Alejandro Mayorkas to head the Department of Homeland Security.