The NSA whistleblower was last year granted temporary asylum of one year, but that ran out on August 1.
His lawyer, Anatoly Kucherena, was quoted by Russian news agencies saying Mr Snowden has been granted residency for three more years.
He said Mr Snowden, who was elected rector of Glasgow University earlier this year, had not been granted political asylum. That status would allow him to stay in Russia permanently but must be decided by a separate procedure, Mr Kucherena said.
He did not say whether his client is seeking it.
Mr Snowden was stranded in a Moscow airport last year en route from Hong Kong to Cuba, shortly after he released extensive documentation about the National Security Agency's surveillance programs.
He reportedly spent a month in the airport before receiving the temporary asylum, but was seen only at one tightly restricted meeting with human rights representatives.
Since receiving the temporary asylum, his whereabouts have not been made public.
The case has been a significant contributor to tensions between Russia and the United States.
"I don't think there's ever been any question that I'd like to go home," Mr Snowden said in a television interview in May.
"Now, whether amnesty or clemency ever becomes a possibility is not for me to say. That's a debate for the public and the government to decide.
"But, if I could go anywhere in the world, that place would be home."