The museum bought the work at an auction in the United States for $US92,500 ($A108,000).

The lips-and-tongue logo was designed by London art student John Pasche in 1970. It was first used on the band's Sticky Fingers album in the following year, and has become part of the Stones' image.

The museum's theatre and performance collections head Victoria Broakes said the design ''... has become arguably the world's most famous rock logo''.

Ms Broakes said the purchase was apt since Pasche used to visit the museum's collections for inspiration when he was a student at the Royal College of Art in London. Jagger, 65, approached the Royal College of Art in 1969 to help him find a design student to counter the bland proposals offered by the band's record label.

Pasche said the idea for the logo came ''when I met Jagger for the first time at the Stones' offices. I went into this sort of wood-panelled boardroom, and there he was. Face to face with him, the first thing you were aware of was the size of his lips and his mouth.'' AP