The veteran rockers narrowly beat mid-week leader Declan McKenna to the top spot, with the 21-year-old singer-songwriter’s second album Zeros losing out by some 800 chart sales.
They also become the first band to score a number one album across six different decades, according to the Official Charts Company.
Sir Mick Jagger, Keith Richards and the rest of the Stones now have 13 number one albums, putting them equal with Elvis Presley and Robbie Williams.
At 15, only The Beatles have achieved more UK number one albums.
Pop Smoke was at three with Shoot For The Stars, Aim For The Moon while Nines was at four with Crabs In A Bucket and Taylor Swift took fifth place with Folklore.
Elsewhere, R&B veteran Billy Ocean debuted at number 14 with One World, his eighth top 20 album and first of new music in seven years.
On the singles chart, Cardi B and Megan Thee Stallion claimed a second week at number one with their paean to female sexuality, WAP.
The song finished with 62,000 chart sales, including 8.1 million streams, earning a strong lead of 12,000 chart sales.
US rapper 24kGoldn moved up two places with Mood featuring Iann Dior, landing at number two.
British rapper Headie One also scored a career best with Ain’t It Different featuring AJ Tracey and Stormzy at number three.
