United confirmed the capture of the 21-year-old on Sunday (AEST) after lengthy negotiations with Palace.
Wan-Bissaka made his Eagles debut against Tottenham Hotspur in February 2018, making a further six appearances during the final months of that campaign.
Hodgson saw enough to make the England Under-21 international his first choice right-back for the 2018-2019 season and he did not disappoint, swiftly establishing himself as one of the most promising defenders in the Premier League.
After his switch to Old Trafford, Wan-Bissaka saluted Hodgson for giving him an opportunity in the senior ranks.
"I would like to thank the youth coaching staff and first-team staff for helping me massively to develop into the player I am today," he wrote on Instagram.
"Most importantly, I would like to thank Roy Hodgson for giving me the opportunity I have always dreamed of, which was to play in the Premier League.
"The faith and trust he had in me led me to have the chance to take my development to a next level."
Palace chairman Steve Parish was quick to praise Wan-Bissaka, saying: "He is a really fantastic young man and we have all enjoyed having him as part of the club for the past 10 years.
"He is a shining example of what south London is about and I wish him the very best for the future journey with Manchester United and England."
💬 "It's an honour for me to play for this club. I can't wait to get out there." — @AWBissaka— Manchester United (@ManUtd) June 29, 2019
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