Fosu-Mensah, 19, joins fellow Dutchman Frank de Boer at Selhurst Park where he becomes the third summer signing following Ruben Loftus Cheek and Jairo Riedewald's arrivals from Chelsea and Ajax respectively.
"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 official 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 joined United's academy from Ajax as a 16-year-old and broke into the first-team under Louis van Gaal during the 2015-16 season at Old Trafford. While he was retained as a member of the first-team squad by Jose Mourinho last term, he started just one game in the Premier League on the final day of the season while making seven more appearances across the Europa League, FA Cup and EFL Cup.
The Dutch youngster had been expected to provide cover for Antonio Valencia down the right this season but the decision to allow him to leave on loan could indicate United's transfer business is not done yet.
According to Goal, Paris Saint-Germain right-back Serge Aurier is poised to sign a five-year deal with the Old Trafford club to compete with Valencia down the right flank. One potential stumbling block in the move however is whether the Ivory Coast international is given permission to enter the UK amid an ongoing legal issue.
The former Toulouse starlet was given a suspended two-year prison sentence for attacking a police officer in 2016, an incident which saw him barred from entering the UK last November when his visa application revoked by the Home Office, ahead of a Champions League tie with Arsenal.
Aurier is awaiting the outcome of an appeal and if granted, he will be free to complete a move to a Premier League side, with Dani Alves expected to become PSG's first-choice right-back following his arrival from Juventus this summer.
United have made three signings this summer in the form of Victor Lindelof, Romelu Lukaku and Nemanja Matic, although Mourinho remains hopeful of making a fourth addition.