The deal was signed for an undisclosed amount and is for a period of seven years beginning from the 2014-2015 season.
Forbes magazine recently called Manchester United the most valuable club in sport (worth $2.23 billion, around £1.43 billion).
Chevrolet will become the clubs fifth shirt sponsor in the club's history.
United's commercial director Richard Arnold said that the deal was a "fantastic, long term deal for the club".
He continued to say that they have been a key partner on the club's current preseason tour and that he knows that they have enjoyed the buzz from the club's fanatical support and the sell out crowds on their preseason travels to South Africa, China and Europe. Chevrolet signed the deal to become the club's car sponsor in May of this year and has also signed a similar deal with United's rivals from Mersyside, Liverpool.
Earlier this month, the club applied to be listed on the US stock market in an attempt to reduce the debt that has accumulated at the club since the take over by the Glazer family, who own the Tampa Bay Buccaneers American football franchise.