The north London club announced the moves on Monday, with European clubs still able to move players to Turkish teams even though the European transfer window closed on Friday.
Sanchez has not started any of Tottenham's opening four games under new manager Ange Postecoglou, who had said he wanted to trim a bloated squad.
Tottenham did not disclose the transfer fee for Sanchez, a Colombia centre-back who had been with the London club for six years and made 207 appearances after joining from Ajax.
Ndombele joins Galatasaray on loan for the remainder of the season, with the option to make the move permanent.
It is Ndombele's third consecutive loan spell away from Spurs since he joined in 2019.