"Charlie was a cherished husband, father and grandfather and also as a member of the Rolling Stones one of the greatest drummer of his generation," a statement posted on Twitter by the Rolling Stones said.
"We kindly request that the privacy of his family, band members and close friends is respected at this difficult time."
A cause of death wasn't released.
Overall, Watts remained healthy throughout his career despite a bout with throat cancer in 2004 and substance abuse in the 1980s.
The band announced earlier this month that Watts was unable to travel with the 2021 No Filter tour following a medical procedure.
"For once my timing has been a little off," Watts said at the time. "I am working hard to get fully fit but I have today accepted on the advice of experts that this will take a while."
The New York Times described Watts as "reserved, dignified and dapper" and his jazz-inflected swing as key to the band's success.
Watts was born on June 2, 1941, in London to Charles Richard Watts, a truck driver and World War II Royal Air Force veteran, and Lillian Charlotte Eaves, a homemaker.
He started playing jazz at age 12 and worked as a graphic artist and played drums with various jazz combos at night after graduating from the Harrow School of Art in 1960.
In 1963, he joined Richards, singer Mick Jagger, guitarist Brian Jones, bassist Bill Wyman and pianist Ian Stewart in the Rolling Stones and contributed a defining sound in songs such as "(I Can't Get No) Satisfaction," "Paint It, Black," "Ruby Tuesday" and "Honky Tonk Women." He also contributed his design skills to the band's stage sets, merchandise and album covers.
Watts mostly eschewed the flashy pop idol lifestyle and married Shirley Anne Shepherd in 1964. The couple had a daughter, Seraphina, in 1968 and bred Arabian horses on their farm in England.
Celebrities posted condolences on Twitter.
"A very sad day," Elton John said on Twitter. "Charlie Watts was the ultimate drummer. The most stylish of men, and such brilliant company. My deepest condolences to Shirley, Seraphina and Charlotte. and of course, The Rolling Stones."
Watts is survived by his wife and daughter.