Mick Jagger, Keith Richards and Ronnie Wood are said to have signed the contract last month, according to insiders cited by The Sun newspaper.
"The story of the Rolling Stones is coming to the big screen," a source told The Sun.
"The band love what 101 Studios have done before and think they're in safe hands. It's early days but the deal is done.
"No casting has started. How the film will look and feel, and the stories it will tell, is being organised now."
Earlier this year, Jagger admitted he had thought about a biopic "a lot", and he is keen for an actor in their 20s to play him when he first shot to fame.
Speaking to E Talk, he said: "I have thought about it, a lot, and the problem with casting is that I want the beginning of getting famous in there. I don't wanna ignore that part.
"I was only 19, 20, and what happens is, they always cast someone (who is) 32 playing 19. I don't want that, I want them to be in their 20s. At least in their 20s."
The 83-year-old rocker also wants a "pretty unknown actor" to portray him in a movie.
He added: "It would be a pretty unknown actor, it wouldn't be a big star actor, on the cusp of being famous.
"They'd have to have that energy and sort of innocence as well of the world of show business of what's going to happen to you and the madness and fun of it all."
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