Video report by ITV News Correspondent Emma Murphy
The prime minister was among the first world leaders to secure a call with the Democrat since his victory in the November 3 election, which Donald Trump is controversially continuing to contest.
The former vice president’s warnings over Brexit have prompted concerns that Mr Johnson may have a strained relationship with the man who will take over the White House in January.
Mr Johnson congratulated Mr Biden on his election win over current President Trump.
The pair also discussed climate change and promoting democracy.
Mr Johnson said on Twitter: "I just spoke to @JoeBiden to congratulate him on his election.
"I look forward to strengthening the partnership between our countries and to working with him on our shared priorities - from tackling climate change, to promoting democracy and building back better from the pandemic."
However, in both the tweet from Mr Johnson and a statement released by Number 10, no mention was made of discussions on Brexit and upholding the Good Friday Agreement.
Yet, in a statement released by Joe Biden's team, the president-elect is said to have "reaffirmed his support for the Good Friday Agreement in Northern Ireland".
A Number 10 source later clarified that the pair did talk "about the importance of implementing Brexit in such a way that upholds the Good Friday Agreement, and the PM assured the president-elect that would be the case".
The incoming US leader, who is of Irish ancestry, has warned that a trade deal with the US is “contingent” on there being no return to a hard border on the island of Ireland amid unease over the prime minister’s controversial Brexit legislation.
The Democrat also warned that the peace process must not “become a casualty of Brexit” in a warning over the controversial UK Internal Market Bill.
Mr Johnson is thought to have been the first European world leader Mr Biden has spoken to since his election win.
A swift call with the incoming president is highly-coveted but it will be particularly welcomed by Mr Johnson amid concerns the pair could face diplomatic difficulties.
The pair have never met before, but Mr Biden has likened the prime minister to a “physical and emotional clone” of Mr Trump.
And, unlike Mr Trump, his successor is not a natural ally of Brexit.
In other controversies, allies of Mr Biden, who was Barack Obama’s vice-president, have not forgiven Mr Johnson for highlighting the first African American president’s “part-Kenyan” heritage, claiming it had given him an “ancestral dislike of the British empire”.
Canadian Prime Minister Justin Trudeau was the first world leader to have spoke with the president-elect.
French President Emmanuel Macron was the third world leader to have received a call from Mr Biden - Mr Johnson took his call at 4pm, while Mr Macron got his around 30 minutes later.
Irish premier Micheal Martin earlier tweeted to say he had spoken to Mr Biden, but the tweet was swiftly deleted and it was later revealed the call had not yet taken place.
A statement from Downing Street said: “They discussed the close and longstanding relationship between our countries and committed to building on this partnership in the years ahead, in areas such as trade and security – including through NATO.
“The Prime Minister and President-elect also looked forward to working closely together on their shared priorities, from tackling climate change, to promoting democracy, and building back better from the coronavirus pandemic.
“The Prime Minister invited the President-elect to attend the COP26 climate change summit that the UK is hosting in Glasgow next year. They also looked forward to seeing each other in person, including when the UK hosts the G7 Summit in 2021.”