The Wales international has penned a contract at Old Trafford running until June 2028, with the club holding an option for an additional 12 months. His arrival makes it two new faces in the space of 24 hours, coming hot on the heels of Brazilian midfielder Andrey Santos' switch to the club.
Darlow, 35, was available for nothing after his deal at Elland Road expired at the end of last season, and he turned down the offer of fresh terms from Leeds to head across the Pennines. He made the number one shirt his own at Elland Road last term, keeping five clean sheets, and brings 279 senior appearances with him, 74 of them at Premier League level.
The veteran is expected to compete with Senne Lammens for the gloves as Michael Carrick's side prepare for a return to Champions League football next season.
Announcing the move, the club's new goalkeeper said he could not wait to get started.
"I am extremely proud to sign for Manchester United. I'm joining an excellent group of goalkeepers and I'm really looking forward to all pushing each other to ensure that we maintain the highest standards, which this club demands.
"This is a really special opportunity; everyone can see what an exciting time it is for the club and I cannot wait to play my part in supporting my team-mates and helping to drive the group forwards."
Director of football Jason Wilcox believes the goalkeeper's character was central to the club's decision to move for him.
"Karl has proven his ability to perform at the highest level, his work ethic and determined personality make him a really strong addition to our squad.
"We are delighted to add a player of his quality and experience to our excellent goalkeeping group."
Darlow's arrival is the latest step in a summer overhaul between the posts at Old Trafford. Andre Onana has returned to Trabzonspor after spending last season on loan with the Turkish club, while back-up Altay Bayindir has been attracting interest from Besiktas and Fenerbahce.
For Leeds United, meanwhile, the departure is a blow, with the club having hoped to persuade their first-choice goalkeeper of last season to stay on at Elland Road.