The American businessman, who also owns American football franchise Tampa Bay Buccaneers, passed away on Wednesday.
A statement on the Buccaneers' website confirmed: "The Tampa Bay Buccaneers are saddened to announce the passing of Owner/President Malcolm Glazer earlier this morning at the age of 85."
Glazer purchased United in 2005, with the Red Devils going on to win five Premier League titles, the Champions League and the Club World Cup under his stewardship.
And the club expressed expressed their condolences to the Glazer family in a short statement on their website, which read: "The thoughts of everyone at Manchester United are with the Glazer family tonight following the news that Malcolm Glazer has passed away.
"Malcolm leaves behind his wife Linda, six children and 14 grandchildren. Staff at Manchester United extend deep and sincere condolences to them all at this difficult time."