The Spanish goalkeeper, David de Gea is departing at the end of his contract, with the club not willing to match the £375,000-per-week deal he signed in 2019.
But the 32-year-old leaves on a personal high, having just won his second Premier League Golden Glove for the most clean sheets in a season.
In a message on social media, De Gea thanked United fans for their support, but said: "Now, it's the right time to undertake a new challenge, to push myself again in new surroundings."
When De Gea's contract expired last Friday, United said they remained in talks with the Spain goalkeeper.
That followed reports that De Gea had signed a contract extension only for the club to withdraw that offer and come back with reduced terms.
United have been linked with a move for Inter Milan keeper Andre Onana.
De Gea wrote: "I would like to express my unwavering gratitude and appreciation for the love from the last 12 years. We've achieved a lot since my dear Sir Alex Ferguson brought me to this club.
Longevity
David De Gea made 415 Premier League appearances, with only six goalkeepers featuring more times in the division.
That is particularly impressive when you consider De Gea played 57 times in La Liga for Atletico Madrid before joining United and, at the age of 32, could have another 200 league appearances ahead of him.
Former England keeper James tops the list on 572 games - and also the list of goals conceded (665) as a result.
Schwarzer follows next on 514 games, and also for goals conceded (653). The Australian has the record for most Premier League appearances of any non-British player.
Republic of Ireland icon Shay Given played 451 times for Blackburn, Newcastle, Manchester City, Aston Villa and Stoke, conceding 607 goals. Brad Friedel, who played for Liverpool, Blackburn, Villa and Tottenham, is next on 450 games (567 goals).
Cech played 443 times - only letting in 366 goals - with Jaaskelainen next on 436 games (613 goals).
De Gea conceded 446 goals in his 415 English top-flight games.
Trophies
After playing in an underwhelming Manchester United team for so long, De Gea cannot compete with some of his rivals for trophies.
He won one Premier League title, in Sir Alex Ferguson's last season in charge in 2012-13. United legend Peter Schmeichel and current Manchester City keeper Ederson have a record five Premier League winners' medals each.
De Gea also won one FA Cup, two EFL Cups and the Europa League - hauls also overshadowed by Schmeichel and Ederson.
Clean sheets
Only three goalkeepers have ever kept more Premier League clean sheets than De Gea - with former Chelsea and Arsenal man Petr Cech top by far with 202.
Former Liverpool, Aston Villa, West Ham, Manchester City and Portsmouth keeper David James is second on 169.
Mark Schwarzer, who played for Middlesbrough, Fulham, Chelsea and Leicester, is next on 151, with De Gea on 147.
De Gea's 17 clean sheets last season took him above David Seaman, Nigel Martyn, Pepe Reina, Brad Friedel, Tim Howard and Edwin van der Sar.
For clean sheets at one club, De Gea is second to Cech and his 162 for Chelsea.
Saves
David De Gea is ranked third for Premier League saves since Opta started recording that data in 2003-04 - so no comparison can be made with earlier-era goalkeepers.
In those 19 years, former United and current Wrexham keeper Ben Foster tops the way with 1,248 saves - aided by longevity and playing for some of the league's weaker teams like Watford, Birmingham and West Brom.
Finn Jussi Jaaskelainen, who played for Bolton and West Ham, is next on 1,223.
De Gea follows on 1,157 (2.8 saves a game), just above Schwarzer, Cech and current West Ham keeper Lukasz Fabianski.
Since De Gea's United debut, his 72% save ratio in the Premier League is only below Cech, Liverpool's Alisson and Newcastle's ex-Burnley keeper Nick Pope (of players to make 100 or more appearances).
Individual trophies
David De Gea won two Premier League Golden Gloves, in 2017-18 and the season just gone. He is one of only six keepers to win it more than once.
Leading the way on four are Cech and Celtic's Joe Hart, who played for Manchester City, Birmingham, West Ham and Burnley.
Ederson and Pepe Reina, who played for Liverpool and Aston Villa, have three, and Alisson has two.
De Gea has a joint record four Manchester United player of the season awards (2014, 2015, 2016 and 2018), level with Cristiano Ronaldo. Nobody else has more than two.
How does David de Gea compare with other United keepers?
United's top three goalkeepers in the Premier League era are widely considered to be Denmark's Schmeichel and the Netherlands' Van der Sar - who each won a Champions League for the club - plus De Gea.
Schmeichel won five Premier League titles to Van der Sar's four and De Gea's one.
De Gea, with 147, beat the pair for clean sheets, though. Van der Sar kept 132 and Schmeichel had 128 - both including for other clubs.
With David De Gea and defender Phil Jones leaving the club this summer, no players left at United have played under legendary manager Ferguson or won the title with the club.