The prime minister congratulated Mr Biden during the phone call on Saturday night, No10 said in a statement.
He also raised the prospect of reaching a fair trade deal between the UK and US “as soon as possible”.
Following the discussion, Mr Johnson tweeted: “Great to speak to President Joe Biden this evening. I look forward to deepening the longstanding alliance between our two countries as we drive a green and sustainable recovery from Covid-19.”
Downing Street said Mr Johnson “warmly welcomed” Mr Biden’s decision to re-join the Paris Agreement on climate change and the World Health Organisation, reversing the decisions made by his predecessor Donald Trump.
“They noted the significant challenges facing the world during the pandemic but also the unparalleled opportunities to build back better and greener together,” a spokesperson said.
“The prime minister praised president Biden’s early action on tackling climate change and commitment to reach net zero by 2050.
“Building on the UK and US’ long history of cooperation in security and defence, the leaders recommitted to the Nato alliance and our shared values in promoting human rights and protecting democracy.
“They also discussed the benefits of a potential free trade deal between our two countries, and the prime minister reiterated his intention to resolve existing trade issues as soon as possible.
“The leaders looked forward to meeting in person as soon as the circumstances allow, and to working together through the G7, G20 and COP 26 this year.”
Mr Johnson has attempted to play down suggestions of a rift with the new president as a result of his close relationship with Donald Trump and his previous remarks about Barack Obama.
In recent days he has refused to comment on a description of the president as “woke” and his decision to remove a bust of Sir Winston Churchill in the Oval Office. He has previously suggested that Barack Obama’s removal of the bust in 2016 was “a snub to Britain” which might be prompted by the “part-Kenyan” president’s ancestral dislike of the empire.
Mr Biden, who once described Mr Johnson as a “physical and emotional clone of Trump”, had calls on Friday with Canadian prime minister Justin Trudeau and Mexican president Andres Manuel Lopez Obrador.