Boris Johnson has said there is “more that unites than divides” him and Joe Biden as he pledged to work together to defend “common values and interests”.
The UK prime minister told broadcasters he and the US president-elect shared a belief in democracy, human rights, free speech and free trade.
He also welcomed the “real prospect” of the US now showing “global leadership” on climate change.
Mr Biden’s allies have meanwhile sought to smooth over Brexit differences.
Senator Chris Coons, who is tipped to become secretary of state in the Biden administration, said the election was an opportunity “to jump start a new chapter” in transatlantic relations.
Asked about Mr Biden’s opposition to Brexit when he was Barack Obama’s vice-president and his subsequent criticism of Mr Johnson, he said he expected there to be some “reconsideration of whatever comments may have been made about the moment of Brexit” in the coming weeks and months.
Following Mr Biden’s victory, Foreign Secretary Dominic Raab said the UK would “listen carefully” to US concerns about the impact of the UK’s departure from the EU on stability on the island of Ireland and the Good Friday Agreement.
Mr Biden has vowed to unify the US after he was declared the winner of the presidential election on Saturday.
The Republican incumbent, President Donald Trump, who is a strong supporter of Brexit, has yet to concede defeat and is taking legal action in a number of states, alleging voting irregularities.
Mr Raab told the BBC’s Andrew Marr that the UK had always had faith in the integrity of the US electoral system to produce a “clear” outcome, which he said it had now done.
“We want to avoid getting sucked into domestic American politics but it is very clear now, in our view, that there is a definitive result,” he said.
He said the British embassy in Washington had been in touch with the Biden campaign and he believed the president-elect and Mr Johnson, who have never met before, would speak in “due course”.
Mr Johnson used his interview to reaffirm the importance of the relationship between the two countries, saying he and the new president had “crucial stuff” to get on with.
“The United States is our closest and most important ally, and that has been the case president after president, prime minister after prime minister – it won’t change,” he said.
“I think there is far more that unites the government of this country and governments in Washington at any time and any stage than divides us.
“We have common values, we have common interests, we have common global perspective. There is a huge amount of work we need to do together to protect those values.”
Mr Johnson signalled that he hoped Mr Biden’s victory would mark a big shift in US policy on climate change, Mr Trump having taken the country out of the Paris Climate Accord.
“I think now with President Biden in the White House in Washington we have the real prospect of American global leadership in tackling climate change,” he said.
The UK and US are currently seeking to negotiate a bilateral trade agreement, against a backdrop of historic tensions with senior Democrats in Congress over Brexit and its impact on Northern Ireland.
Mr Biden has warned that the 1998 Good Friday Agreement must “not be a casualty” of Brexit and expressed concerns about the UK government’s attempt to pass legislation that would give it the power to override aspects of the EU Withdrawal Agreement with regard to Northern Ireland.
What a Biden presidency means for the UK
The election of Joe Biden leaves Boris Johnson facing a substantial diplomatic repair job. The two men have never met.
Last December the president-elect described the prime minister as a “physical and emotional clone” of Donald Trump.
There are people around Mr Biden who remember bitterly how Mr Johnson once suggested President Obama harboured anti-British sentiment because of his part-Kenyan ancestry.
Mr Biden and his team think Brexit is a historic mistake. They would not want Britain to leave the EU without a trade deal, particularly if it involved breaking commitments made in the Northern Ireland protocol.
Mr Johnson has expressed his belief that the UK will be able to secure mutually beneficial trade agreements with both the US and the EU, its two largest partners.
But he has also signalled that he will now bow to pressure from the EU to re-write the Internal Market Bill, which is due to be voted on in the Lords on Monday, to take out controversial clauses
“The whole point of the Internal Market Bill… is to protect and uphold the Good Friday Agreement and the peace process in Northern Ireland,” he said.
“That is one of the things that we’re united on with our friends in the White House.”
Asked about Mr Trump’s continued claims that he had won the election, the foreign secretary said the UK and other foreign countries must be careful not to be seen to be seeking to interfere in the election or its aftermath.
He added: “I am sure Donald Trump and his team will reflect on where they lie.”