"It is with immense sadness that we announce the death of our beloved Charlie Watts," a statement said.
It said he was "a cherished husband, father and grandfather" and "one of the greatest drummers of his generation".
Tributes have come from stars including The Beatles' Sir Paul McCartney and Sir Ringo Starr, and Sir Elton John.
Sir Paul described Watts as "a lovely guy" and "a fantastic drummer" who was "steady as a rock".
Sir Elton wrote on Twitter: "A very sad day. Charlie Watts was the ultimate drummer. The most stylish of men, and such brilliant company."