Spurs will pay £25m upfront, with £10m in add-ons agreed with Brighton. The Mali International has agreed a deal that will run until 2026.
Head coach Graham Potter said, “The transfer is a very good one for the club and player.
“Yves has shown his undoubted ability and been an important player for us during his time with us.
“Now he has a new challenge with Tottenham, including the opportunity to play Champions League football, and everyone at the club wishes him well.”
The 25-year-old Mali international brings an end to a four-year spell on the south coast.
Yves joined Albion from Lille for £15m in 2018, going onto make 124 appearances in all competitions, scoring on six occasions.
He made his Albion debut on the opening day of the 2018/19 season at Watford. He scored his first Premier League goal against Burnley on the final day of the 2019/20 campaign.
Last season he made 26 Premier League appearances, as Albion finished ninth in the top-tier – the highest position in the club’s history.
Bissouma said: “It has always been my dream to play to play Champions League football with Tottenham. We have a good group and a great coach.”
Meanwhile, Brighton left-sided defender Marc Cucurella continues to be linked with a move to Manchester City. Pep Guardiaola is said to be a huge admirer of Spain star who enjoyed a fine first season in the Premier League.