The 35-year-old arrives after deciding against extending his stay at Leeds United, despite being offered fresh terms when his contract expired earlier this summer. Leeds confirmed his departure without mentioning his move to their Premier League rivals.
"Leeds United can confirm Karl Darlow has left the club upon the expiration of his contract to pursue an opportunity elsewhere," Leeds said in a statement.
"Despite the offer of a new deal to remain in West Yorkshire, the goalkeeper wished to explore a different challenge and leaves the Whites with the best wishes of everyone at Elland Road."
Darlow finished the previous campaign as Daniel Farke's first-choice goalkeeper and brings significant experience to Old Trafford, having made 279 club appearances and collected 15 senior caps for Wales.
The veteran shot-stopper is expected to serve as deputy to Senne Lammens, who is currently on a three-week break following Belgium's FIFA World Cup campaign.
"I am extremely proud to sign for Manchester United," Darlow said.
"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."
With Lammens unavailable, Darlow is likely to feature during Manchester United's pre-season programme, which gets underway against Wrexham in Helsinki on 18 July.
Belgium international Youri Tielemans said he "feels incredible" after penning a five-year contract to join Manchester United from fellow Premier League side Aston Villa.
Manchester United have confirmed the signing of Andrey Santos from Chelsea, while the Red Devils are also closing in on a deal for the transfer of Youri Tielemans from Aston Villa.
Manchester United are preparing to ramp up their pursuit of new midfielders this week after identifying four leading candidates, with the club aiming to recruit two more in the current transfer window.
Chelsea are reportedly willing to listen to offers for Alejandro Garnacho just 12 months after signing the Argentine winger from Manchester United.
