The father-of-three died on Tuesday surrounded by his family, the army said in a statement posted on X.
Born into a military family on 21 March 1944, he joined the army at the age of 19 before graduating from Birmingham University in 1967.
At the height of the Cold War he learnt Russian in the Intelligence Corps.
In 1970 he transferred to the Parachute Regiment, serving in Northern Ireland during the Troubles.
He later attended the Ballymurphy inquest, where he denied there was a “cover-up” over the shooting of 10 people.
Sir Mike rose to command the regiment’s First Battalion between 1984 and 1986.
Between 1995 and 1996 he commanded the UN peacekeeping force in Bosnia.
During the Kosovo campaign he was awarded the Distinguished Service Order for leadership.
He became head of the British Army just a month before the Iraq war began, replacing Gen Sir Michael Walker.
He is survived by three children from two marriages and four grandchildren.
Paying tribute to his memory, the Parachute Regimental Association said he had been a “great leader of men” who would be “missed by many”.
