The Tory grandee was Margaret Thatcher’s longest-serving Cabinet minister - but was widely held to have ended her premiership with a devastating resignation speech in 1990.
A statement issued by his family said: “It is with deep sadness that the Howe family today announced that Geoffrey Howe died suddenly late yesterday evening, aged 88, at his home in Warwickshire, of a suspected heart attack, after enjoying a local jazz concert with his wife Elspeth.
“There will be a private family funeral, followed by a memorial service in due course. The family would be grateful for privacy at this time.”
Mr Cameron described Lord Howe as a “kind, gentle and deeply thoughtful man” who had “never stopped giving strong and sound advice”.
“The Conservative family has lost one of its greats,” the Prime Minister added.
Mr Cameron said: “Geoffrey Howe was a kind, gentle and deeply thoughtful man - but at the same time he had huge courage and resolve.
“His time as Chancellor of the Exchequer was vital in turning the fortunes of our country around, cutting borrowing, lowering tax rates and conquering inflation. Lifting exchange controls may seem obvious now, but it was revolutionary back then. He was the quiet hero of the first Thatcher government.
“He loved his politics and never stopped giving strong and sound advice. George Osborne and I benefited greatly from his wisdom and determination to improve the state of the country. The Conservative family has lost one of its greats. Our thoughts are with his family.”
Lord Howe became Chancellor after Mrs Thatcher won the 1979 general election, and was a key figure in many of her most controversial economic reforms.
In her second term he was made Foreign Secretary, grappling with how to handle dramatic developments in South Africa - and the increasingly thorny issue of Britain’s relationship with Europe.
In 1989, amid growing tensions with Mrs Thatcher over Europe, he was shifted to the more junior position of Leader of the House of Commons.
He was, however, also given the title of Deputy Prime Minister.
He resigned in November 1990, shortly after the PM declared that the UK would never join a single currency project.
In his devastating departure speech in the Commons, he criticised Mrs Thatcher for undermining policies on economic and monetary union in Europe that were backed by her colleagues and the Governor of the Bank of England.
“It is rather like sending your opening batsmen to the crease, only for them to find, as the first balls are being bowled, that their bats have been broken before the game by the team captain,” he declared.
Three weeks later Mrs Thatcher resigned after failing to prevent a Tory leadership contest going beyond the first round.