Mick Jagger, Keith Richards, Charlie Watts and Ronnie Wood, who this year are celebrating the band's 50th anniversary, will play two dates at London's O2 arena and two at Brooklyn's new Barclays Center, which has yet to be completed.
News of the shows comes after the band members initially said they would not tour this year, then hinted at upcoming gigs during a book launch and photography exhibit in London last month marking their anniversary.
A spokeswoman for the band was not immediately available for comment or confirmation.
A new documentary, announced earlier this month in Los Angeles, also is in the works.
Called "Crossfire Hurricane" and directed by Brett Morgen, it promises new footage and insights from the band and will open in cinemas in Britain before being broadcast on the BBC and then HBO in the United States.
The Stones, who last toured in 2005-2007 with their top-grossing "Bigger Bang" show, were formed in London in 1962 and are one of the longest-performing rock bands in the world. They have sold an estimated 200 million records worldwide.
