Yves Bissouma scored against Tottenham in the FA Cup last season
The 25-year-old becomes Spurs boss Antonio Conte's third summer signing, following deals for goalkeeper Fraser Forster and winger Ivan Perisic.
Bissouma, whose contract with the Seagulls expires in 12 months, has made 124 appearances since joining the club from Lille in July 2018.
The north London club were initially interested in signing him in January.
He is expected to undergo a medical at Tottenham later this week and the deal is subject to personal terms being agreed with the player.
The coveted central midfielder started 26 Premier League games for the Seagulls last season, scoring once.
He played an influential role in Graham Potter's side as they secured ninth place in the Premier League - the highest finish in the club's history.
Bissouma said last September it was not his time to leave Brighton but that he wanted to play in the Champions League, which Spurs have qualified for next season.
-- Courtesy of BBC Sport