Anatoly Kucherena said Snowden left Moscow's Sheremetyevo airport Thursday, where he was stuck since his arrival from Hong Kong on June 23.
Kucherena said that Snowden's whereabouts will be kept secret for security reasons.
The United States had demanded Russia send Snowden home to face prosecution for espionage, but Russia dismissed the request.
Russian President Vladimir Putin had said that Snowden could receive asylum in Russia on condition he stops leaking U.S. secrets. Kucherena has said Snowden accepted the condition.
The Associated Press contributed to this report.