Joe Biden has said it is "time to turn the page" after his presidential election victory was confirmed by the US electoral college.
In a speech after the announcement, he said US democracy had been "pushed, tested and threatened" and "proved to be resilient, true and strong".
He condemned President Donald Trump's attempts to overturn the result.
Later Russian President Vladimir Putin became one of the last world leaders to congratulate Mr Biden on his victory.
Moscow had said it would wait for the official results before doing so. Most other national leaders contacted Mr Biden days after the vote on 3 November.
Confirmation by the electoral college was one of the steps required for Mr Biden to take office.
Under the US system, voters actually cast their ballots for "electors", who in turn formally vote for candidates after the election.
Democrat Joe Biden won November's contest with 306 electoral college votes to Republican Donald Trump's 232.
President Trump, who shows few signs of conceding, has not commented. Shortly after the electoral college's vote, he announced on Twitter the departure of Attorney General William Barr, who had said there was no evidence of widespread voter fraud in the election, despite the president's claims.
'Flame of democracy'
Speaking in Delaware, Mr Biden praised "ordinary men and women" who had refused to be bullied, referring to the president's efforts to question and overturn the results, involving legal challenges which have been rejected by courts across the country.
He described the efforts as "a position so extreme we've never seen it before".
"Respecting the will of the people is at the heart of our democracy, even when we find those results hard to accept," he said.
"The flame of democracy was lit in this nation a long time ago," he added. "And we know that nothing not even a pandemic or an abuse of power can extinguish that flame."
Mr Biden said it was time to "turn the page, as we've done throughout our history, to unite, to heal".
But he warned that, with the coronavirus pandemic continuing to ravage the US, there would be difficult months ahead.
"There is urgent work in front of us," he said. "Getting this pandemic under control and getting the nation vaccinated against this virus."
He stressed the importance of immediate economic help that was "so badly needed by so many Americans who are hurting today" and rebuilding the economy to be "better than it ever was".
He was speaking as the Covid death toll in the US - the country worst affected by the virus - rose above 300,000.
What happened at the electoral college?
Normally the electors do not get that much attention but this year, after uncertainty generated by a raft of challenges to results in Democrat-won states by the Trump campaign, the state-by-state vote was in the spotlight.
Solidly Democrat California, with its 55 electors, was one of the last states to vote on Monday and took Mr Biden across the 270-vote threshold required to win the presidency.
Heightened security had been put in place in some states, including Michigan and Georgia, ahead of voting, which took place in state capitals and Washington DC.
In Michigan - a key swing state Mr Biden won - legislative offices in the state capital Lansing were closed due to "credible" threats of violence.
The vote at the capitol building went ahead peacefully although a group of Republicans tried to enter the building to hold their own vote and were turned away.
In his speech, Mr Biden described the harassment of officials following the election as "unconscionable" and said: "It's my sincere hope we never again see anyone subjected to the kind of threats and abuse we saw in this election."
He also noted that he had the same number of electoral college votes that Mr Trump said was a "landslide" when he won in 2016. Mr Biden emphasised that he had also won the popular vote, something Mr Trump failed to clinch four years ago.
Republican Senator Lamar Alexander said: "The presidential election is over. States have certified the votes. Courts have resolved disputes. The electors have voted. I hope that President Trump will put the country first, take pride in his considerable accomplishments, and help president-elect Biden get off to a good start."
Curtain lowered on Trump court challenges
The quadrennial meeting of the US electoral college is usually a formality along the way to a presidential inauguration - a vestigial political event that long ago lost its power and relevance.
Donald Trump's scorched-earth strategy of contesting the results of the 2020 election, however, gave the proceedings new attention.
His legal team has had little success in challenging the results in multiple battleground states and the official recording of the electoral college ballots effectively lowered the curtain on these long-shot judicial manoeuvres.
That does not mean the Trump team is giving up, of course. They will continue with futile court challenges and, eventually, ask Congress to overturn the election results.
It is an alternative reality that Donald Trump's supporters may find more comforting than the one where Joe Biden is president-elect.
Given that the House of Representatives is controlled by Democrats, the official electoral college tally has been duly certified by the states and federal law is on Mr Biden's side, Mr Trump's chances of success in the real world, however, sit squarely at zero.
What happens next?
The results of the voting process will be sent to Washington DC and formally counted in a joint session of Congress on 6 January presided over by Vice-President Mike Pence.
That will pave the way for Joe Biden to be sworn in as president on 20 January.
Last month, President Trump said he would leave office in January if Mr Biden were affirmed as the election winner by the electoral college. Nevertheless, he has continued to make unsubstantiated claims of election fraud.
Most Republicans have stood behind Mr Trump in his efforts to overturn the result, but some have broken ranks in recent weeks.
One Michigan congressman, Paul Mitchell, announced he was leaving the party weeks before his retirement in protest over what he said was its failure to accept that the election process was over.