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The Glazer family purchased United for £790m in May 2005 amid protests from the Premier League club's fans.
However, they went on to win five Premier League titles and the Champions League under his ownership.
The New York-born American's sons, Joel and Avram, took over the day-to-day running of the club after their father suffered a stroke in April 2006, said BBC.
"The thoughts of everyone at Manchester United are with his family tonight," said a spokesman for the Premier League club.
The Glazer family retain a 90% share in United - split equally among Glazer's six children - with 10% listed on the New York Stock Exchange.
Glazer, who never actually stepped foot inside Old Trafford, gradually bought out United shareholders between 2003 and 2005.
His takeover was largely funded by loans secured against the club's assets, a move that took them heavily into debt and sat uneasily with many fans at Old Trafford.
Manchester United Supporters' Trust vice-chair Sean Bones said: "It would be inappropriate for me to make any comment about the death of Malcolm Glazer as I didn't know him or his family personally.