Despite repeated attempts, the rock group has never before been granted permission to play in Russia. They were denied permission in 1967 and again a decade later.
About 160 rock fans from the heart of Siberia flew to Moscow on Tuesday to see the Stones' first - and only - concert in Russia, an airline spokesman said.
The fans took a four-hour flight from Novosibirsk to see the concert at the 83,000-seat Olympic stadium in Moscow, said Dmitry Manakov of the private carrier Sibir airlines.
"Most of them are old fans of the Stones and now they finally have a chance to see their idols," Manakov said.
He said the fans planned to catch a return flight straight after the concert.