Gregg died peacefully in a hospital, surrounded by family, The Harry Gregg Foundation said Monday.
A former Northern Ireland international, Gregg spent nine years with Manchester United after joining as the world's most expensive goalkeeper in 1957. He played 247 times for the club, including in a victory in an FA Cup match against Sheffield Wednesday 13 days after the air crash in February 1958.
The team was returning from a European Cup game when their airplane crashed after refueling in Munich. Gregg escaped the wreckage, having sustained only a bloody nose, but returned on two occasions to help teammates Bobby Charlton and Dennis Viollet and then a 20-month-old girl and her badly injured mother.
Gregg also helped revive United manager Matt Busby, who survived the disaster. Eight United players died in the crash.
"He will always be remembered for what he did at Munich," Charlton was quoted as saying by the BBC, "but on top of that he was a really great goalkeeper."
In his autobiography, called "Harry's Game," Gregg said the air disaster in Munich "established my identity" but "the notoriety has come at a price."
"For Munich has cast a shadow over my life which I found difficult to dispel," he wrote.
United said Gregg's contribution to United "could never be underestimated."
"Although it has been said many times before, we will not see his like again," the club said. "In short, he was, without question, one of the great figures in United's history and his name and deeds, both on and off the field, will always be remembered and revered."
Gregg was part of the team rebuilt by Busby after the Munich disaster but never won a medal with United, injury having ruled him out of the win over Leicester in the 1963 FA Cup final and restricting his appearances in two title-winning campaigns , in 1964-65 and 1966-67.
"A real tough nut," United said of its former 'keeper, "Gregg was vocal, commanding and abrasive."
He left Old Trafford for a brief spell at Stoke before an underwhelming managerial career, when he was in charge of Shrewsbury, Swansea, Crewe and Carlisle.
Gregg played 25 times for Northern Ireland, including at the 1958 World Cup, when he was selected as the best goalkeeper in the competition.
When Windsor Park in Belfast was officially reopened following development in 2016, Gregg was afforded a warm on-field ovation by the fans as well as meeting boxing champion Carl Frampton and golfer Rory McIlroy.
Four years earlier, then-United manager Alex Ferguson brought a full-strength squad to Windsor Park to face an Irish League XI in honor of Gregg, whose career at United ended without a testimonial.
In his program notes, Ferguson described Gregg as "beyond legendary" and "a most reluctant hero."
Gregg was awarded an OBE in the 2019 New Year Honours.