Sexton died on Saturday night, former Chelsea goalkeeper Peter Bonetti said. Chelsea did not disclose the cause of death, but club historian Rick Glanvill said he had been suffering from dementia.
During his period as Chelsea manager between 1967 and 1974, Sexton followed up the FA Cup triumph over Leeds in 1970 with a European Cup Winners' Cup final victory over Real Madrid the following year.
"He passed away peacefully last night," said Bonetti, who played under Sexton. "I've spoken to his wife and it's come as a complete shock because he was such a lovely man.
"Everybody loved him and everybody respected him here at Chelsea and he will go down in the club's history as being such a fantastic guy who brought us so much success. He was a football fanatic."
Sexton, whose managerial career began at Leyton Orient, also took charge of Queens Park Rangers, Manchester United for a trophyless four years from 1977, Coventry and England's under-21 team.
"It is a sad day for English football," said English Football Association director of football development Trevor Brooking. "Anyone who was ever coached by Dave would be able to tell you what a good man he was, but not only that, what a great coach in particular he was.
"In the last 30-40 years Dave's name was up there with any of the top coaches we have produced in England — the likes of Terry Venables, Don Howe and Ron Greenwood. His coaching was revered."
Sexton masterminded the victory over Madrid in the 1971 European Cup Winners' Cup final, winning the replay 2-1 after an initial 1-1 draw.
In a tribute on its website, Chelsea praised Sexton for turning a "dynamic, volatile" team into trophy winners while pioneering new technology.
"(He) brought a flexibility to tactics and lineups that we'd never seen before," Glanvill, the club historian, said. "Unforgettably, he stewarded the 'King's Road swingers' to glory in the 1970 FA Cup and 1971 Cup-Winners' Cup — that replay, outfoxing Real Madrid, being arguably his finest tactical game."
"In later years it was a tragedy that such a brilliant mind was clouded by dementia," Glanvill added.