The Colombia international, 21, has signed a contract with the Club until 2023.
The defender moved to Ajax from Colombian club Atletico Nacional in June, 2016 and made 47 appearances for the Dutch side, scoring seven goals.
Sanchez won Ajax’s ‘Rinus Michels’ Player of the Year Award in his only season at the Club, which was previously won by Jan Vertonghen in 2012 and Rafael van der Vaart in 2002.
He made his professional debut for Atletico Nacional aged 17 and was part of their Copa Libertadores winning side in 2016.
Having represented his country at Under-17, Under-20 and Under-23 levels, Sanchez made his senior Colombia debut in November, 2016 and has made two appearances for the national side.
Davinson 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."