The trade agreement was negotiated for twelve years by twelve countries around the Pacific with the aim of countering China.
The main objective of the deal is to cut trade tariffs - a form of tax, like a border tax - between member countries.
International Trade Secretary Liz Truss will formally request today for Britain to join the Comprehensive and Progressive Agreement for Trans-Pacific Partnership (CPTPP), a market representing half a billion people and roughly 13.5% of the global economy.
Some 95% or more of tariffs are to ultimately be abolished in trade among members.
That unwieldy acronym stands for the Comprehensive and Progressive Agreement for Trans-Pacific Partnership.
She plans to speak to Japan's economy minister Yasutoshi Nishimura and Damien O'Connor, New Zealand's minister for trade and economic growth, by video call on Monday.
Donald Trump withdrew from negotiations to join the trade alliance in 2017 but amid the rise of China, Mr Biden has indicated the United States may join the group.
CPTPP membership will complement and reinforce new and enhanced bilateral trade agreements we have already signed or are negotiating now - with Australia, Canada, Chile, Japan, Mexico, New Zealand, Peru, Singapore and Vietnam.
The UK is set to be the first to make a formal request following the entry into force of the CPTPP, he said, and will serve as an important precedent which "reinforces the commitment of new members to fully deliver the high standards, including on market access, that are a hallmark of the CPTPP".
The Biden administration, which has been cautious about rejoining, is expected to prioritize the pandemic response and other domestic issues.
The US buys more than double the amount of United Kingdom exports than all of the current CPTPP nations put together.
"One year after our departure from the European Union we are forging new partnerships that will bring enormous economic benefits for the people of Britain", said Prime Minister Johnson.
Truss said the deal will mean lower tariffs for vehicle manufacturers and whisky producers, and would also deliver "quality jobs and greater prosperity for people here at home".
It may be on the other side of the world, but that's not stopping the United Kingdom from applying to join a trade partnership in and around the Pacific Ocean.
The government said joining the FTA, whose other members are all around the Pacific, would raise tariffs on food, drink and cars while helping boost the technology and service sectors.
"We're at the front of the queue and look forward to starting formal negotiations in the coming months", Truss was quoted as saying in a statement.