McConnell later warned Republicans in his conference not to object to the Electoral College outcome when Congress affirms Biden's victory on Jan. 6, multiple sources told NBC News.
The Kentucky Republican congratulated the incoming Democratic president after the Electoral College formally certified Biden's victory on Monday. Numerous GOP senators did not acknowledge Biden as the election winner for more than a month as President Donald Trump made baseless claims that widespread election fraud cost him a second term in the White House.
"Our country has officially a president-elect and a vice president-elect," McConnell said on the Senate floor on Tuesday.
"The Electoral College has spoken. So today I want to congratulate President-elect Joe Biden" and Vice President-elect Kamala Harris, he continued.
Biden on Tuesday morning told reporters he spoke to McConnell after the Republican congratulated him. The president-elect said he told the senator he believes they can work together and hopes the pair can meet sooner rather than later.
McConnell congratulated Biden after running through a list of what he called "nearly endless" accomplishments during Trump's term as president. He pointed to policies including the 2017 GOP tax law and "perhaps most importantly" the confirmation of three conservative Supreme Court justices.
Speaking after McConnell recognized Biden's win, Senate Minority Leader Chuck Schumer, D-N.Y., said Republican officials should "follow Leader McConnell's lead and acknowledge now that Joe Biden will be the next president of the United States."
GOP senators including Susan Collins of Maine and Mitt Romney of Utah congratulated Biden shortly after it became apparent he would win the presidential election last month. Others such as Sen. John Thune of South Dakota, the No. 2 Republican in the chamber, publicly accepted the reality as the Electoral College voted Monday.
Still, some including GOP Sens. Kelly Loeffler and David Perdue of Georgia have refused to accept Biden's win. Both lawmakers will try to keep their seats in Jan. 5 runoffs that will determine whether McConnell and the GOP keep control of the Senate.
The day after that special election, the House and Senate are set to count the electoral votes in a joint session, presided over by Vice President Mike Pence. Any objections to those votes must be submitted in writing and signed by at least one House member and one senator. If an objection is made, the two chambers will consider the objection separately.
Such a move would likely fail, and some Republicans, including Romney, have already rejected the idea of attempting to challenge the election in its final stage.
In a conference call Tuesday, McConnell, along with Missouri Sen. Roy Blunt and Senate Majority Whip John Thune of South Dakota, warned senators not to object to the results, multiple sources told NBC.
Doing so would be a "terrible move" for Republicans, who would then have to defy Trump on the record by voting against the objection, McConnell reportedly said. No senators so far have objected to McConnell's request, NBC reported.
If Republicans hold the chamber, McConnell will have massive influence over what his former Senate colleague Biden can accomplish in the White House. Biden's top priorities including a massive coronavirus relief package, a public-health care option and a green-energy focused infrastructure plan will likely face GOP resistance.
Trump has vowed never to concede to Biden. He is falsely claiming he won the race and is spreading a bevy of unproven, debunked and baseless conspiracy theories as he argues that he was robbed of reelection by massive electoral and voter fraud.
Trump, in his first tweet following McConnell's acknowledgement of Biden's win, again asserted his claims of voter fraud without addressing the Republican Senate leader's remarks. On Tuesday afternoon, White House press secretary Kayleigh McEnany told reporters she has not "gotten the president's reaction" to McConnell's comments yet, but noted Trump is "pursuing ongoing litigation." Trump's lawyers have repeatedly failed to prove systemic election fraud in court.
Even after the Electoral College cast its votes to make Biden's win official, Trump continued to amplify his false claims on Twitter.
"Tremendous problems being found with voting machines," he tweeted Tuesday morning, providing no evidence. "Able to take a landslide victory and reduce it to a tight loss," he falsely tweeted.
Attempts from Trump's campaign and his allies to reverse Biden's win have failed in dozens of court challenges. The U.S. Supreme Court on Friday delivered what appeared to be a fatal blow to those efforts, when it declined to hear a long-shot bid from Texas Attorney General Ken Paxton to invalidate the results of four key swing states that voted for Biden.
More than 100 House Republicans, including House Minority Leader Kevin McCarthy of California, backed the Texas lawsuit.
Trump had called Paxton's far-fetched case "the big one," despite a broad consensus of election law experts predicting its failure was inevitable.
But neither the devastating court loss nor the Electoral College defeat appear to have tempered the president's comments, the most incendiary of which have been aimed at GOP officials in Georgia. Biden narrowly won the state.
On Tuesday morning, Trump retweeted a post from attorney Lin Wood predicting that Georgia's Republican Gov. Brian Kemp and Secretary of State Brad Raffensperger "will soon be going to jail."
Trump's promotion of Wood marks a potentially consequential clash with his party ahead of the two pivotal runoff elections in the Peach State.
Wood, who along with lawyer Sidney Powell has lodged numerous failed court bids alleging election fraud, is calling for a boycott of those runoffs. Republican lawmakers pushed back fiercely, accusing Wood of being a Democratic operative attempting to depress GOP turnout for Perdue and Loeffler.
McConnell's announcement came hours after a Kremlin statement said Russian President Vladimir Putin had sent a telegram to Biden wishing "every success to the president-elect."