Last week, Ajax confirmed that Sanchez would depart for a transfer fee of €40 million (£36.6m) that could rise to €42m with add-ons depending on appearances and success.
The Colombia global has agreed a six-year deal and will wear the number six shirt for Mauricio Pochettino's side.
Sanchez has put pen to paper on a deal until 2023 for a reported club-record £42million fee.
Spurs' previous record was the £30m paid to Newcastle for France midfielder Moussa Sissoko in 2016.
Ajax have raked in a huge profit on the 21-year-old - who signed for just £4m from Colombian outfit Atletico Nacional just last summer.
He is the second arrival at Tottenham on Wednesday after Spurs announced the signing of goalkeeper Paulo Gazzaniga from Southampton - who will become their third-choice stopper.
The 25-year-old, who started his career at Valencia before moving to England with Gillingham in July 2011, said: "This is an wonderful club and the facilities are unbelievable".
Also, Swansea began spending some of the 45 million pounds (then $58 million) the club received from Gylfi Sigurdsson's move to Everton last week by signing midfielder Sam Clucas from Hull, which was relegated from the Premier League in May.