As Conservative Party chairman under Thatcher in the early 1980s, Lord Parkinson played a key role in the Tories' 1983 general election victory.
He was elevated to the Cabinet in 1981 but had to quit a few years later after it emerged his former secretary, Sara Keays, was carrying his child.
Despite the scandal, he returned to the government in 1987 serving as energy and then transport secretary.
A family spokesperson said: "We shall miss him enormously. As a family, we should like to pay tribute to him as a beloved husband to Ann and brother to Norma, and a supportive and loving father to Mary, Emma and Joanna and grandfather to their children.
The politician was central to Thatcher's political agenda and was also part of her war cabinet during the Falklands War in 1982.
He left the House of Commons in 1992 and briefly made a comeback as Conservative Party chairman after the Tories' general election hammering in 1997.