Fosu-Mensah completed his move on Thursday to become Frank de Boer's third addition of the transfer window after the arrivals of Jairo Riedewald and Ruben Loftus-Cheek.
The versatile 19-year-old, who will wear the number 24 shirt at Selhurst Park, was a youth-team player at Ajax when De Boer was in charge of the Eredivisie side.
"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," Fosu-Mensah told Palace's 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."
Fosu-Mensah made his United debut in February 2016 and has gone on to make 21 appearances across all competitions.
He is under contract with United until 2020 after agreeing a new deal last season, but will now seek to gain further first-team experience with Palace.
De Boer said: "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."
As they also confirmed the news, United insisted Fosu-Mensah was "highly regarded" at Old Trafford and wished him well for the upcoming season.
Palace begin their Premier League campaign at home to promoted side Huddersfield Town on Saturday.