Sanchez has joined Galatasaray as the same day that Tanguy Ndombele also makes the same switch, from Spurs to the Turkish side.
Ndombele has signed for Galatasaray on a loan deal with an option to buy, but Sanchez has joined the Turks permanently.
Galatasaray have confirmed that they will pay €9.5m (£8.1m) for Sanchez and the fee will be paid in five instalments.
It had been claimed at the English end that Tottenham will pocket £12.8m, but Galatasaray are insisting that they are paying £8.1m for Sanchez.
The Colombian defender had entered the final year of his contract at Tottenham and signed a four-year deal, with an option for a further year, in Turkey.
Spurs boss Ange Postecoglou was happy to let him go given the other options he has in his squad.
Galatasaray were keen to get Sanchez signed up today in order to register him in their Champions League squad.