The 35-year-old, who was out of contract at Elland Road at the end of June and failed to agree a new deal, was announced by the Red Devils on Tuesday afternoon as their latest summer signing.
Darlow said he is “extremely proud” to sign for United and hopes to “maintain the highest standards” at the club who have shown faith in him.
The veteran was Daniel Farke’s No.1 last season but will be second choice at Old Trafford behind Senne Lammens as he prepares for minimal game time.
After making his move, Darlow took to Instagram and sent a message to Leeds fans as he wished the club all the best heading into the new campaign.
“To Leeds United, what a special chapter this has been. Helping this club achieve promotion back to the Premier League is something I’ll always be proud of, and to know the club will be staying where it belongs makes it even more rewarding.
“To my teammates, coaches, staff and everyone behind the scenes, thank you for making my time here so memorable. I leave with amazing memories, friendships, and immense pride in having played a part in this club’s journey.
“To the fans, thank you for the incredible backing. Your passion for this club is truly unmatched! It’s been an honour to represent you all. I’ll be watching on from afar and wishing everyone connected with Leeds nothing but success. Thank you for everything. Darlow.”
Darlow turned down interest from Middlesbrough and Hull City to sign for United where he will likely be handed a chance during cup games.