Bissouma has signed a four-year contract for an initial £25m transfer fee.
The Mali international's deal at Brighton would have expired next summer.
Tottenham's two previous signings had all been free transfers with Ivan Perisic and goalkeeper Fraser Forster joining from Inter Milan and Southampton respectively.
The 25-year-old midfielder told the club website: 'It's my dream to play Champions League when I was younger. I remember I was watching Champions League everyday and I can't believe to play Champions League with Spurs.
'I'm so happy. Thank you to my mum, dad and my agent here. Thank you to everyone. Thank you to Spurs as well.'
Bissouma joined Brighton from Lille in the summer of 2018 and made 124 appearances across all competitions for the Seagulls, scoring six goals.
Brighton manager Graham Potter acknowledged Bissouma's contribution to the club, which included helping them to a best-ever ninth place finish in the Premier League last season, and wished him well.
'The transfer is a very good one for the club and player,' Potter said.
'Yves has shown his undoubted ability and been an important player 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.'
