The former France youth international had joined Galatasaray on a four-year contract in 2021 from Stade Rennais.
He scored his first Champions League goal for the club in a 2–2 draw against Copenhagen on September 20th 2023.
Turkish Super League champions Galatasaray said in a statement that Bayern would pay a fee of 30 million euros ($32.59 million).
"Sacha Boey is a very quick and physically very strong right back who puts in a lot of kilometres in each game and does not shy away from a one-on-one," said Bayern sports director Christoph Freund. "He will improve our defensive quality."
The Bavarians, second in the Bundesliga behind Bayer Leverkusen, have been struggling with a growing list of injury absences including defensive stalwarts Dayot Upamecano and Konrad Laimer, who were injured in their midweek win over Union Berlin and will be out for weeks.
Defensive midfielder Joshua Kimmich was also injured in that game, while defenders Kim Min-jae and Noussair Mazraoui are on international duty and right back Bouna Sarr is also injured.
