The Labour peer served in Number 11 during the 1974-79 government and became the party's deputy leader in 1980 during a career on the frontline of British politics which began in 1952.
He died peacefully at his home in Sussex yesterday morning after a short illness, his family said.
The Labour veteran, often viewed as "the best prime minister the party never had", served as a major in the Royal Engineers in North Africa and Italy.
During the Anzio landings he was a beach master, received the MBE, and was mentioned in despatches.
Lord Healey stood unsuccessfully for election in 1945 and eventually entered the Commons as MP for Leeds South East in 1952.
He reached the Cabinet as defence secretary in 1964, but he will be remembered for his role as chancellor during a turbulent time for the British economy which saw the UK forced to go to the International Monetary Fund for a bailout.
"He was the best leader Labour never had," said Rt Revd Nick Baines.
"He was also the last of a generation of politicians who had a hinterland to their political life.
"Healey represents the last of a generation who brought to our political life a deep experience of human conflict – one that fired his humanity and political life.
"It is only when they have gone that we begin to realise what we have lost."
Lord Healey twice ran for the Labour leadership but was defeated by James Callaghan in 1976 when Harold Wilson quit, and then again in the contest with Michael Foot in 1980 which led to the party's leftward shift in opposition to Margaret Thatcher.