There is speculation that he might now fly on to another country.
Hong Kong said Washington had failed to meet the requirements for extradition.
Mr Snowden, an intelligence contractor, fled to Hong Kong in May after revealing details of internet and phone surveillance by US intelligence.
The Aeroflot flight, SU213, landed in Moscow at 17:10 local time (13:10 GMT).
The Russia 24 TV channel has said Mr Snowden does not have a Russian visa, so will stay in the airport overnight before, the channel says, flying to Cuba on Monday.
A source at the airline company was quoted as saying that, from Cuba, he would fly on to Venezuela. Both countries are believed unlikely to comply with any US extradition request.
Whistleblowing website Wikileaks has issued a statement saying that it has helped to find him "political asylum in a democratic country". » | Sunday, June 23, 2013
