The shows at the O2 Arena in Greenwich take place on 25 and 29 November and they will be called 50 Years & Counting - Rolling Stones Live.
The two shows are the band's first live dates in five years, since the band last played at the same venue to close their Bigger Bang tour.
Mick Jagger commented, "Everybody loves a celebration, and London and New York are two good places to do it in!”
Keith Richards said, ”Sorry to keep you all hanging around but 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!"
Tickets for the dates are on sale on Friday at 9am.
Meanwhile, the band will also play two shows in New Jersey at the Prudential Center, Newark on 13 and 15 December.