It notched up 106,000 combined sales across all platforms - the second highest opening week sales so far this year behind David Bowie's Blackstar.
Blue & Lonesome is the 12th album by The Rolling Stones to reach number one.
The Official Charts Company said 95,000 of the album's sales were physical - the rest were downloads and streams.
It was also the only new entry in this week's top 40.
