The Turkish side were racing to complete the deals before 11pm on Monday, when their squad for the Champions League group-stage had to be registered.
Sanchez’s departure has now been made official after the clubs agreed a total package in the region of £12.8m, with Ange Postecoglou sanctioning the sale, while Ndombele has left on a season-long loan.
Sanchez had entered the final year of his contract at Spurs and looked unlikely to be handed regular starts. The 27-year-old only Premier League involvement this season came when Cristian Romero picked up a head injury against Brentford, while the Colombian missed a penalty in the Carabao Cup shootout defeat to Fulham.
The move to Galatasaray brings an end to Sanchez’s six-year spell as a Tottenham player, after he arrived from Ajax in the summer of 2017. He made 207 appearances during his time in north London, scoring five goals.
Ndombele, who remains Spurs’ record signing, spent last season on loan at Napoli and now gets another temporary move to try and impress, as he and Sanchez join the likes of Wilfried Zaha and Mauro Icardi at the Turkish club.
Galatasaray revealed they have an option to make the deal a permanent one next summer for a £12.8m fee.