Both leaders agreed to remain in personal contact as well, signalling a stepped-up political effort to secure a new trading partnership before Britain ends a post-Brexit transition period on Dec 31.
Conservative former finance minister Sajid Javid echoed his views, calling the election the "best outcome" for Britain and predicting that Johnson had a much better chance of sealing a trade deal under Biden rather than the "protectionist" Trump.
New laws on coronavirus relief, economic recovery, immigration reform, infrastructure improvements and tackling climate change would all be higher priorities.
There is also said to be bad blood between the pair after Mr Johnson commented that Barack Obama, a close friend of Mr Biden after he served under him as vice-president, had an "ancestral dislike of the British empire" due to his "part-Kenyan" heritage.
Labour leader Sir Keir congratulated president-elect Mr Biden, praising his campaign for "decency, integrity, compassion and strength", and predicted the win would see the U.S. play a more central role on the world stage once again.
"Once every vote is counted, President-Elect Biden and Vice President-Elect Harris will have won a historic and decisive victory", Obama, Donald Trump's White House predecessor, said in a statement.
"His extreme Brexit policies, and decision to align himself so closely with the narrow politics of Donald Trump have left the Tory Prime Minister increasingly isolated on the world stage".
It is thought Mr Johnson will emphasise the need for the two nations to work together to combat climate change ahead of the United Kingdom hosting a UN climate summit next year.
Bentley will sell only plug-in hybrids and EVs by 2026
It's part of a new strategy the automaker is undertaking to become the "global leader in sustainable luxury mobility". That is likely to be a version of an electric-only architecture developed by sister firms Porsche and Audi.
'They think Britain is an ally.
He called on Boris Johnson to "reflect" on his own style of politics following President Trump's projected defeat.
But he could be in for a frosty reception from Mr Biden, with a Democratic source telling the Sunday Times: 'They do not think Boris Johnson is an ally.
He too disregarded the suggestion of any difficulties with the new relationship, following claims from some U.S. commentators that previous comments by Mr Johnson on Barack Obama's Kenyan heritage had damaged ties with the Democrats.
In a statement, Foreign Secretary Dominic Raab said: "President Trump fought hard in what proved a close contest".
Johnson also singled out Vice President-elect Kamala Harris for "her historic achievement" as the first woman, first Black woman and first person of South Asian descent to win national USA office.
Sir David Manning, a former British ambassador to the U.S., told Times Radio that Mr Biden "values the bi-lateral relationship" and said a strong relationship with Mr Johnson "should be possible" given the common interests between the longstanding allies.
Asked on Sky News' Sophy Ridge On Sunday whether he was fuelling conspiracists with his response, Mr Raab said: "No, I think that's a very partisan skew on it".