A family spokesman said: "Cecil passed away on January 22 after a long battle with cancer.
"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.
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"We also salute his extraordinary commitment to British public life as a member of parliament, cabinet minister and peer - together with a distinguished career in business."
He added: "There will be a private family funeral. The family requests that their privacy be respected in this matter. Details about a memorial service will be announced later."
Chancellor George Osborne led tributes to the peer, tweeting: "Sad to hear of death of Cecil Parkinson. I worked with him when he was Party Chairman in 1997-8 - he was there in our hour of greatest need."
William Hague, who selected Lord Parkinson as party chairman when he became Tory leader, wrote: "Very sad to hear about the death of my friend Cecil Parkinson. An exceptional talent and an extraordinarily nice man to work with."
