The record-deal, understood to be worth around £25m a year, trumps big money shirt sponsorship deals struck by Liverpool, Barcelona and Bayern Munich.
The deal kicks off at the start of the 2014-15 season, as Manchester United’s current deal with Aon has two more seasons to run.
It is unclear if Aon - whose current sponsorship deal with Manchester United is worth £20m a season - wanted to continue its shirt sponsorship deal.
Manchester United signed a lower-tier deal with the General Motors-owned Chevrolet as official car partner just weeks ago, and last week signed a similar deal with United's arch-rival Liverpool.
Chevrolet is owned by General Motors, which also owns UK car brand Vauxhall, the headline sponsor of the England team.
GM's chief marketing officer Joel Ewanick resigned with immediate effect over the weekend, with a Reuters report quoting an anonymous source claiming Ewanick failed to report proper financial details about the Manchester United sponsorship.
Ewanick has been replaced by Alan Batey, head of US sales and service, while the company searches for a replacement.
Batey said: "We are extremely proud to connect our brand, Chevrolet, with Manchester United and its passionate supporters all around the world.
"Manchester United’s statistics are impressive, but this relationship goes far beyond the numbers – this relationship is about connecting our brand with the deep-seated emotion that surrounds the team everywhere it goes."
Chevrolet will become only the fifth shirt sponsor in Manchester United’s 134-year history.