They made a video (see below) and announced it via their Facebook page - two shows at London's O2 Arena on November 25 and 29, and two at the Prudential Center in Newark, New Jersey on December 13 and 15.
They released a statement, in which Mick Jagger says "Everybody loves a celebration, and London and New York are two good places to do it in". Keith Richards elaborated, saying "The waiting is over. I've always said the best place for rock and roll is on the stage and the same is true for the Stones. I'm here with Mick, Charlie and Ronnie and everything is rocking. See you very soon!"
Prices for London are an eye-watering £106-£406 (causing some consternation amongst fans). Tickets for London go on sale this Friday and for New Jersey next Friday. Full ticket details can be found here.