A key figure in England's sole World Cup triumph in 1966, Charlton won 106 caps for his country and scored 49 international goals - both records that stood for decades.
He also won three league titles, an FA Cup and a European Cup during a 17-year club career with United, having miraculously survived the dreadful Munich air disaster in 1958 that took the lives of eight of his teammates.
He is widely regarded as the greatest English footballer of all time and was knighted for services to football in 1994.
He made his debut for United in 1956 and went on to play 758 matches for the Red Devils, scoring 249 goals. Both were long-standing club records that stood for 40 years until they were overtaken by Ryan Giggs and Wayne Rooney respectively.
Old Trafford's South Stand was renamed the Sir Bobby Charlton Stand in 2020.
Charlton's family said he "passed peacefully in the early hours of Saturday morning".
Manchester United said in a statement that he would forever be remembered "as a giant of the game".
"Manchester United are in mourning following the passing of Sir Bobby Charlton, one of the greatest and most beloved players in the history of our club.
"Sir Bobby was a hero to millions, not just in Manchester, or the United Kingdom, but wherever football is played around the world.
"He was admired as much for his sportsmanship and integrity as he was for his outstanding qualities as a footballer; Sir Bobby will always be remembered as a giant of the game.
"A graduate of our youth Academy, Sir Bobby played 758 games and scored 249 goals during 17 years as a Manchester United player, winning the European Cup, three league titles and the FA Cup. For England, he won 106 caps and scored 49 goals, and won the 1966 World Cup.
"Following his retirement, he went on to serve the club with distinction as a director for 39 years.
"His unparalleled record of achievement, character and service will be forever etched in the history of Manchester United and English football; and his legacy will live on through the life-changing work of the Sir Bobby Charlton Foundation.
"The club's heartfelt sympathies are with his wife Lady Norma, his daughters and grandchildren, and all who loved him."
His former England teammate and now last surviving member of the 1966 winners, Sir Geoff Hurst, said: "We will never forget him and nor will all of football
"A great colleague and friend he will be sorely missed by all of the country beyond sport alone. Condolences to his family and friends from Geoff and Judith."
In 2020, it was announced Charlton had been diagnosed with dementia.
His family reported that he died peacefully during the night surrounded by loved ones, and they wanted to "pass on their thanks to everyone who has contributed to his care and for the many people who have loved and supported him".
