Senate Majority Leader Mitch McConnell has congratulated Democrat Joe Biden as president-elect, saying "the Electoral College has spoken".
The Republican leader's statement, delivered in a speech on the Senate floor on Tuesday, ends weeks of silence over Donald Trump's defeat.
It also comes a day after electors met and officially affirmed Mr Biden's election win.
"I want to congratulate president-elect Joe Biden," Mr McConnell said.
"Many of us had hoped the presidential election would yield a different result.
"But our system of government has the processes to determine who will be sworn in on January 20. The Electoral College has spoken."
Mr McConnell described Mr Biden as someone "who has devoted himself to public service for many years".
He also congratulated vice president-elect Kamala Harris, saying "all Americans can take pride that our nation has a female vice president-elect for the very first time".
Mr McConnell prefaced his remarks with sweeping praise for what he characterised as Mr Trump's "endless" accomplishments during four years in office.
He said Mr Trump and vice-president Mike Pence "deserve our thanks".
The Senate leader cited Mr Trump's nomination and ensuing Senate confirmation of three Supreme Court justices, among other accomplishments.
Mr McConnell's remarks follow a groundswell of leading Republicans who have said for the first time that Mr Biden is the winner of the presidential election, essentially abandoning Mr Trump's assault on the outcome after the Electoral College certified the vote.
For his part, Mr Trump continued to push his claims of "voter fraud" in a new tweet on Tuesday.
With states affirming the results, the Republicans faced a pivotal choice – to declare Mr Biden the president-elect, as the tally showed, or keep standing silently by as Mr Trump waged a potentially damaging campaign to overturn the election.
Their turnaround comes nearly six weeks after election day.
Many Republicans rode out the time in silence, enabling Mr Trump to wage an unprecedented challenge to the voting system.
Some have vowed to carry the fight to January 6 when Congress votes to accept or reject the Electoral College results, while others have said Mr Trump's legal battles should continue towards resolution by inauguration day on January 20.
"It's a very, very narrow path for the president," Republican senator Lindsey Graham said.
"But having said that, I think we'll let those legal challenges play out."
Earlier on Tuesday, Russian president Vladimir Putin also congratulated Mr Biden after weeks of holding out.
The Kremlin had previously said the Russian president would hold off on congratulating Mr Biden until the winner was officially confirmed.
In his message, Mr Putin wished Mr Biden "every success", according to a Kremlin statement.
He expressed confidence "Russia and the US, which bear special responsibility for global security and stability can, despite the differences, really contribute to solving many problems and challenges that the world is currently facing".
The Russian president noted "the Russian-American co-operation based on the principles of equality and mutual respect would meet the interests of the people in both countries and the entire international community".
He added: "For my part, I am ready for interaction and contact with you."