Illingworth famously led England to a 2-0 Ashes series victory in Australia in 1970-71. He played 61 Tests for his country between 1958 and 1973 - 31 of those as captain - scoring 1,836 runs at an average of 23.24 and claiming 122 wickets at 31.20.
The cricketing legend also enjoyed a hugely successful domestic career with Yorkshire and Leicestershire.
After finishing his playing career, Illingworth served as England's chairman of selectors between 1994 and 1996 and coached the national team in 1995-96.
England and Wales Cricket Board chief executive Tom Harrison said in a statement: "It's always incredibly sad to lose a person who has given so much to the English game, and to the sport of cricket in general.
"Ray was a superb cricketer, and his deep love, passion and knowledge for the game meant he continued to contribute long after his playing days had finished. We send our sympathy and warmest wishes to Ray's friends and family at this difficult time."
Michael Atherton, who captained England during Illingworth's controversial stint as selector and coach, with the pair failing to see eye to eye, also paid tribute.
He said on Twitter ahead of the Boxing Day Ashes Test: "Hope England can put on the kind of tough, shrewd performance that Ray Illingworth would have enjoyed."
Illingworth's first-class career spanned a remarkable 32 years from his debut in 1951 to his final appearance in 1983.
He finished with a final total of 24,134 first-class runs and 2,072 wickets and was named a Wisden Cricketer of the Year in 1960.
He played for Yorkshire from 1951 to 1968, leading them to three successive County Championship victories in those final three years, before joining Leicestershire in 1969, remaining at Grace Road until 1978.
He returned to Yorkshire initially as team manager but made his playing comeback at the age of 50 in 1982.
Yorkshire paid tribute to "the club's most successful modern-day captain".
"We are deeply saddened to learn that Ray Illingworth has passed away," the county said in a statement.
"His success at county level was matched on the international scene, enjoying a long career with England as captain.
"Our thoughts are with Ray's family and the wider Yorkshire family who held Ray so dear to their hearts."
The club's chairman Lord Patel described Illingworth as "one of Yorkshire's, and England's, greatest players".
He said: "He had a significant, and lasting, impact, and will be fondly remembered by fans of cricket across the county and the nation. My heart goes out to his family and all who knew him."
Leicestershire said on Twitter: "Everybody at Leicestershire County Cricket Club are deeply, deeply saddened to hear of the passing of former Captain, Ray Illingworth.
"Our thoughts are with Illy's family and friends at this difficult time."
Marylebone Cricket Club, of which Illingworth was an honorary life member, also said it was "deeply saddened" to learn of his death.
Farsley Cricket Club, Illingworth's local side for whom he first played as a teenager and where he would prepare wickets well into his 70s, said cricket had "lost a great".
They added on Twitter: "Absolute LEGEND of a man you will be sorely missed by many!"
Illingworth's wife Shirley died earlier this year after battling cancer and Illingworth had offered his support for law changes over assisted dying.
"I don't want to have the last 12 months that my wife had," he said. "She had a terrible time going from hospital to hospital and in pain.
"I believe in assisted dying. The way my wife was, there was no pleasure in life in the last 12 months, and I don't see the point of living like that, to be honest.
"But we don't have assisted dying in England yet, so you don't have the option do you? They are debating it and I think it will come eventually.
"A lot of doctors are against it, but if they had to live like my wife did in her last 12 months they might change their minds."