The shows mark the first time in five years that the Stones have performed live, with Mick Jagger, Keith Richards, Charlie Watts and Ronnie Wood all coming together once more. The band said it was the "crowning glory" of celebrations marking its 50th anniversary of its first gig.
"Everybody loves a celebration, and London and New York are two good places to do it in!" Jagger said in a statement.
The Stones have sold more than 200 million records, with hits including "(I Can't Get No) Satisfaction," ''Street Fighting Man" and "You Can't Always Get What You Want."
But in recent years much of their income has come from touring. Their last global tour, "A Bigger Bang," earned more than $500 million between 2005 and 2007.
Their legions of fans will hear era-defining tracks such as "Gimme Shelter," ''Jumping Jack Flash," ''Tumbling Dice," ''It's Only Rock and Roll," plus a few surprises and other classics from GRRR!, the multiformat album coming out in November.
"GRRR!" is a greatest hits collection that includes two new songs "Doom and Gloom" and "One More Shot," recorded recently in Paris — the first new recordings since the 2005 album "A Bigger Bang."
The band promises an all-new, custom-built set design, featuring the tongue and floppy lip logo, that will "reach out into the crowd." A wider tour is not planned, though the Dec. 15 performance will be available on pay per view.
The tour comes despite some famously testy times.
Richards and Jagger have been creative catalysts and sparring partners — sentiments aggravated two years ago when Richards published his autobiography "Life."
They've nonetheless appeared amicably together during events that marked their 50th anniversary. A documentary about the band, "Crossfire Hurricane," premieres at the London Film Festival on Thursday.
In another milestone marking their five decades of music, the Museum of Modern Art in New York will host "The Rolling Stones: 50 Years on Film," a retrospective chronicling the band from the mid-1960s until today. This exhibition will be open Nov. 15.