The Londoner, who made his name playing for Fulham in the 1950s, enjoyed a second career as a distinguished broadcaster.
He died after suffering from Alzheimer's disease for a number of years.
In a statement, Jane Morgan, spokeswoman for Hill's wife Bryony, said: "It is with great sadness that Bryony Hill and the children of Jimmy Hill have announced that Jimmy passed away peacefully today aged 87 after a long battle with Alzheimer's disease. Bryony was beside him."
In 1961, after retiring from playing football at the age of 33, Jimmy Hill became manager of Coventry City. His time at the club was nicknamed 'The Sky Blue Revolution' due to the changes he brought in.
Under Jimmy Hill the team won the Division Three championship in 1963-1964, and the Division Two title in 1966-1967. He left the club before the start of the 1967-1968 season.
Stars from the world of football spoke of Hill's contribution to the game following the announcement of his death.
Current MotD presenter Gary Linker led the tributes.
He wrote on Twitter: "Deeply saddened to hear that Jimmy Hill has left us. A football man through and through who gave the game so much in so many ways #RIPJimmy."
BBC pundit and former England striker Alan Shearer said: "Very sad news about Jimmy Hill. Footballers and football have so much to thank him for. A man who loved the game."
Tony Hall, director-general of the BBC, said: "For generations of fans Jimmy Hill was an authoritative voice as both a presenter and analyst. He was committed to innovation in every aspect of the game, including broadcasting, and always believed supporters came first. His influence lives on in the programmes we enjoy today."
Hill will be cremated at a private ceremony.
A service for his friends and colleagues will be held in the new year, Ms Morgan said.