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, his agent, Jane Morgan, 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."
Hill will be cremated at a private ceremony.
A service for his friends and colleagues will be held in the new year, his agent said.
Hill started his career at Brentford in 1949, where he made 87 appearances before moving to Fulham three years later.
Hill scored 52 goals in close to 300 games for the Cottagers and became the chairman of the Professional Footballer's Association in 1957, where he made a significant impact.
During his spell as PFA chairman, Hill successfully campaigned for the abolition of the £20-a-week maximum wage and to introduce freedom of contract.
After his retirement at the age of 33 in 1961 he took his only managerial role at Coventry City and changed the club's strip colour to sky colour and Hill also introduced the first-ever colour match programme in English football.
He led the club the the Division Three championship in 1963-84 and the the Division Two title three years later but he quit the club shortly after before the start of their top-flight campaign.
Hill was the Head of Sport at ITV between 1968 and 1972, a spell which including fronting the coverage of the 1970 World Cup in Mexico.
He moved to the BBC in 1973 where he became the host of Match of the Day before Des Lynam took over the reins in 1989.
He made more than 600 appearances on the show as both a presenter and analyst.
BBC director general Tony Hall 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."
BBC director of sports Barbara Slater added: "Jimmy Hill was an iconic and unique figure and we are all deeply saddened by the news.
"He was one of the great innovators and a huge talent, a man ahead of his time with a personality that dominated his era both in football and broadcasting.
"Jimmy was also a dear friend and colleague to many at the BBC and will be greatly missed."
Current match of the day presenter Gary Lineker also paid tribute to Hill, saying on his Twitter account: "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."
Source : PA
Source: PA