Lord Brittan, 75, served as home secretary from 1983 to 1985 and president of the Board of Trade in 1985/86, before spending a decade in Brussels from 1989 to 1999 one of the UK’s European commissioners, and as vice-president of the Commission from 1989 to 1993.
He was MP for Cleveland & Whitby from 1974 to 1983 and for Richmond, Yorkshire, from 1983 to 1988.
His family said there will be a private funeral service for family only, and a memorial service will be announced.
Lord Brittan was thrust into the headlines in July last year by questions over his handling of a dossier handed to him as home secretary in 1983 by Tory MP Geoffrey Dickens, alleging the existence of a paedophile ring at Westminster.
The former home secretary confirmed that he had a meeting with Mr Dickens and was given a file, which he passed on to officials, adding: “I do not recall being contacted further about these matters by Home Office officials or by Mr Dickens or by anyone else.”
However, the department later released an extract of a letter Lord Brittan sent to Mr Dickens the following March explaining that the material had been assessed as worth pursuing by the director of public prosecutions (DPP) and was “now being passed to the appropriate authorities”.
An independent review commissioned by the Home Office in 2013 found that the department had not retained the dossier.
A furore over the allegations led to an independent review of the Home Office’s handling of child abuse allegations in the 1980s by NSPCC chief executive Peter Wanless, whose report last November found no evidence of a cover-up - but warned it was impossible to draw firm conclusions.
A second, more wide-ranging, inquiry into official handling of abuse claims was also commissioned by Home Secretary Theresa May, but its proposed chair Fiona Woolf stood down after questions were raised about her social links with Lord Brittan, who was a near neighbour.
Lord Brittan was a Home Office minister in Mrs Thatcher’s first government in 1979 and joined the Cabinet as chief secretary to the Treasury in 1981. His appointment as home secretary in 1983 made him the youngest person to hold the post since Sir Winston Churchill.
His tenure at the Home Office saw the siege at the Libyan People’s Bureau in London during which WPc Yvonne Fletcher was shot, and the controversial deployment of police in large numbers during the national miners’ strike.
Within months of his move to the Department of Trade and Industry in 1985, he became caught up in the row over helicopter company Westland which eventually led to his resignation and that of then defence secretary Michael Heseltine.
Following a heated dispute within the Cabinet over whether the Somerset-based company should link up with an American or European backer, Lord Brittan resigned in 1986 after being forced to apologise to Parliament over a letter which he had denied receiving from British Aerospace. This was followed by the revelation that he had authorised the leak of a law officer’s letter.
His career in Brussels also ended with a resignation, when he and the other members of Jacques Santer’s Commission quit en masse amid allegations of fraud.
Lord Brittan continued to serve as vice-president for a few months under interim president Manuel Marin, but was then replaced by Chris Patten.
Lord Brittan was made a life peer in 2000, and took up positions in business, serving as vice-chairman of the UBS investment bank from 2000-14. He was a trade adviser to Prime Minister David Cameron following the formation of the coalition Government in 2010.
Former Tory leader William Hague, who succeeded Lord Brittan as Richmond MP, led tributes to the former home secretary.
Commons Leader Mr Hague said: “He was a kind, assiduous and brilliant man. I know the whole House will join me in sending our deepest condolences to his wife Diana at this difficult time.”
Former chancellor Lord Lamont said: “I’m very sorry to hear the sad news of the death of Lord Brittan.
“He was a man of great brilliance who would have risen to the top of whatever profession he had chosen.
“He was also a very kind and good man.
“He did an outstanding job as an EU commissioner in Brussels, handling all the complex trade issues with a great mastery of detail.”