The 19-year-old has played 21 times for the Red Devils, but made just three starts and seven substitute appearances in all competitions last season.
Fosu-Mensah, a Netherlands Under-21 international, trained with his new teammates on Thursday morning and was unveiled as a new signing later in the afternoon.
"The manager spoke to me about coming down to join Crystal Palace and it was clear that he wanted me to be part of his squad which as a player gives you a great feeling straight away," he told the official Eagles website.
"I must now repay that back by putting in some good performances for the club. I am only 19 years old and still have a lot to learn and therefore getting the opportunity to play more games on a regular basis will help my development."
Palace manager Frank de Boer added: "Timothy is a player who has great pace and incredible physical ability. In today's game you need players with strength and speed and is a player who can also play in midfield. I am seeing him in our system as a right centre-back but he can also play full back in a 4-3-3."