The 21-year-old Colombian centre-back is Spurs' first signing of the transfer window and has penned a contract running until 2023.
Sanchez's switch is subject to a medical and granting of a work permit, with Ajax receiving an initial €40m before potential add-ons.
"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," Sanchez told Tottenham's official website.
"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."
We are delighted to announce we have reached agreement with Ajax for the transfer of Davinson Sanchez subject to medical & work permit. pic.twitter.com/bCjP3ur3Ca— Tottenham Hotspur (@SpursOfficial) August 18, 2017
Sanchez began his career with Atletico Nacional in his homeland, making his professional debut at 17 and helping them to Copa Libertadores glory in 2016 before joining Ajax in June of last year.
In November he was capped for the first time for Colombia at senior level and starred as part of the Ajax side that reached the final of the Europa League. He made 47 appearances for the Eredivisie giants and scored seven goals
Ajax's director of player policy, Marc Overmars, said: "Last week, many conversations were held with Davinson and Spurs' business observers. We did not want to let him go.
"When we came to this huge amount and it was clear that Davinson would leave, I consulted with my colleagues in the club leadership.
"We have jointly decided that the transfer period for outgoing transfers has now been closed. We will not let anyone [else] go."
Ajax head coach Marcel Keizer voiced similar sentiments earlier Friday, indicating he expected Sanchez to depart but believed the club would retain their other young stars.