The American was granted temporary asylum of one year in the country after leaking tens of thousands of classified National Security Agency documents, but that ran out on August 1.
His lawyer, Anatoly Kucherena, yesterday confirmed Mr Snowden would be given residency in Russia for three more years.
He said his client, who was elected rector of Glasgow University earlier this year, had not been granted political asylum. However, Mr Kucherena said Mr Snowden would be able to extend his residency permit for a further three years when it runs out and after five years would be eligible to apply for Russian citizenship, but he did not know if his client intended to do so.
Breffni O'Connor, president of the Students' Representative Council at Glasgow University, said the body welcomed the decision. She said: "We at the SRC are glad to see our rector Edward Snowden have his residency in Russia extended by three years. This will give him more stability in what you can probably imagine is an understandably less than ideal situation for him.
"The rector has expressed interest in engaging with students on our campus over the next three years in his role, and at the SRC we are involved in efforts to facilitate this communication between students and Edward that will allow him to represent students at Glasgow at the highest level in university governance."
Mr Snowden was installed as rector at a ceremony in Bute Hall in April this year, where he appeared via video link from Russia. He said he could not attend in person because he was banned from entering the UK "on the grounds that my presence is considered detrimental to the public good".
He was voted in ahead of rival candidates cyclist Graeme Obree, author Alan Bissett and Scottish Episcopal clergyman Kelvin Holdsworth.
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 NSA'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 US has filed espionage charges against Mr Snowden, charging him with theft of government property, unauthorised communication of national defence information and wilful communication of classified communications intelligence to an unauthorised person.
The case has been a significant contributor to tensions between Russia and the United States.
Speaking in a television interview in May, Mr Snowden said: "I don't think there's ever been any question that I'd like to go home.
"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."
The residency permit will allow Mr Snowden to travel out of Russia for the first time, so long as he does not stay outside the country for more than three months at a time. Mr Kucherena said he could not say which country his client might visit.
He added: "Of course, he misses his relatives, and coming to terms with his future was difficult for him. He will decide for himself about meeting with them."