Greenhoff made 271 appearances for the Red Devils and won 18 caps.
Born in Barnsley, Greenhoff joined United in 1968 and was part of the United team that won the Second Division title in 1975.
Two seasons later he won the FA Cup, playing alongside brother Jimmy in the Wembley triumph over Liverpool.
Greenhoff subsequently moved to Leeds, where he stayed for three years, before ending his career at Rochdale, where he was living after returning to England from Spain.
A statement released to the Manchester Evening News by Greenhoff's family said: "We regret to inform of Brian's passing this morning, Wednesday May 22 at the age of 60.
"Brian was a proud and much loved brother, husband of Maureen, father of Paul, Brian and Peter, grandfather to Jack, James and Harry and will be sorely missed by his family, who he made very proud in his distinguished life and career."
- Sports & Recreation