The 21-year-old Colombian centre back has put pen to paper on a deal until 2023 for a reported club-record Â£42million fee.
He is the first player to join Spurs this summer and his arrival comes after much debate about the club's transfer policy during the off-season.
In a statement, Tottenham said: "We are delighted to announce that we have reached agreement with AFC Ajax for the transfer of Davinson Sanchez subject to medical and work permit.
"The Colombia international, 21, has signed a contract with the Club until 2023."
The fee is believed to eclipse the previous club record of Â£30million which Spurs paid Newcastle for midfielder Moussa Sissoko last summer.
Sanchez joined Eredivisie side Ajax in June last year on a five-year deal after leaving Atletico Nacional in his homeland.
He played in last season's Europa League final, which Manchester United won 2-0, and was named Ajax's player of the year in May.
Sanchez said: "I would like to thank the coach, management, players and fans of Ajax. It is a great move for me to come here to develop my career.
"I am very excited to be signing for such a famous club as Tottenham Hotspur.
"I am looking forward to working with Mauricio Pochettino and the players and meeting everyone there."
Sanchez has represented Colombia at Under-17, Under-20 and Under-23 levels before making his senior debut in November last year, and has two international appearances.