The German sportswear giant has stepped in after Nike pulled out of negotiations over a new deal last week because it felt United were demanding too much money.
The adidas agreement, described in a statement as "a global technical sponsorship and dual branded licensing deal", will run for 10 years from the 2015-16 season.
The deal with Nike, United's kit manufacturer since 2002, runs out at the end of the forthcoming season.
United believe it is the biggest kit deal in sport, surpassing the likes of Barcelona and Real Madrid as well as major American sports, which tend to sign league-wide deals covering all teams.
A United statement read: "Manchester United plc has reached a 10-year agreement with adidas for a global technical sponsorship and dual branded licensing deal for a minimum guarantee of £750million, subject to certain adjustments, beginning with the 2015/2016 campaign.
"For the 2014/2015 season, Nike will continue in its role of technical sponsor and trademark licensee."
The deal is more than twice as big as the Nike agreement signed in 2002, which was worth £303million with extra income from a profit share agreement from merchandise sold worldwide.
In a statement last week, the sportswear giant said: ''Manchester United is a great club with passionate fans.
''We are proud to have partnered with them for the last 12 years and will continue to sponsor the club until the end of the 2014/15 season.
''Any partnership with a club or federation has to be mutually beneficial and the terms that were on offer for a renewed contract did not represent good value for Nike's shareholders.
''We look forward to a successful final season with the club.''
This season also sees the beginning of US car giant Chevrolet's kit sponsorship deal with United, which is worth a reported £53million per season.
- Sports & Recreation
- Manchester United