Charlton was a key figure in England's 1966 World Cup-winning team, playing alongside his brother Jack, and he made 758 appearances for United, scoring 249 goals.
"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," the Premier League club said in a statement.
Charlton spent 17 years at Old Trafford and, aged 20, was part of the "Busby Babes" team decimated by the 1958 Munich air crash in which 23 people died, including eight United players.
He scored twice for England in the World Cup semi-final win over Portugal in 1966 and was instrumental in the 4-2 victory over West Germany in the final where Geoff Hurst scored a hat-trick.
Hurst, now the only surviving member of Alf Ramsey's World Cup-winning side, led the tributes to his former team mate.
"Very sad news today. One of the true Greats Sir Bobby Charlton has passed away," Hurst wrote on X.
"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."
Charlton helped United win the European Cup in 1968 and three English league titles as well as the FA Cup.
"Today is not just a sad day for Manchester United & England, it's a sad day for football and everything that Sir Bobby represented," said former United and England midfielder David Beckham.
Regarded as possessing one of the hardest shots of his generation and a player whose style bridged eras, Charlton earned 106 caps for England and scored 49 goals.
After his retirement, he served as an ambassador for United and English football and was widely respected across the globe.
Charlton's appearances in the stands at Old Trafford had become less frequent after he was diagnosed with dementia in 2020.
Nowhere will Charlton's death be more keenly felt than at Manchester United where a stand at their Old Trafford ground is named in his honour.
Charlton recovered from the trauma of the Munich air crash and a decade later scored twice as United beat Benfica at Wembley to win the European Cup for the first time.
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Along with his team mates George Best and Denis Law, he helped United became one of the most popular clubs in 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," United said.
"His unparalleled record of achievement, character and service will be forever etched in the history of Manchester United and English football."
Beckham's glittering Manchester United career began after attending a Bobby Charlton Soccer School as a young boy.
"A true gentleman, family man and truly a national hero… Today isn't just a sad day for Manchester United and England it's a sad day for football and everything that Sir Bobby represented," Beckham said.
Manchester City manager Pep Guardiola described Charlton as a "big legend".
"A huge loss for his family and for the Manchester United family and for English football, European football," he said. "We have the Premier League that we have because of these type of people."
United play Sheffield United later on Saturday when the players will wear black arm bands and observe a minute's silence. A book of condolence will be open for fans at Old Trafford on Sunday.
The Football Association said a full tribute will be paid to Charlton at Wembley Stadium when England play Malta on Nov. 17.
"The world of football will unite in its sadness at losing an undisputed legend," England manager Gareth Southgate said.
