Snowden, who leaked information about the National Security Agency's huge monitoring program, was granted temporary asylum, which allows him to stay for as long as a year in Russia, RIA Novosti reported.
"I have just handed over to him papers from the Russian Immigration Service. They are what he needs to leave the transit zone" and enter the country's territory, Russian attorney Anatoly Kucherena said.
He left the transit zone of Moscow's Sheremetyevo International Airport about 30 minutes before the announcement that his temporary asylum request was granted, an RT television crew at the airport said.
Snowden left the airport alone and is at an undisclosed location, Kucherena said.
"He is the most wanted person on earth and his security will be a priority," the lawyer said. "He will deal with personal security issues and lodging himself. I will just consult him as his lawyer."
However, whistle-blowing organization WikiLeaks, which has helped Snowden since he revealed he was the man who leaked the NSA information, said he left with WikiLeaks adviser Sarah Harrison, The Guardian said.
Snowden intends to talk to the media eventually, but needs some privacy, Kucherena said.
The former NSA contractor had been in the transit zone of Sheremetyevo International Airport since June 23, when he arrived from Hong Kong as a transit passenger.
Snowden faces several charges in the United States, including two espionage-related charges. The United States has urged Russian leaders to send Snowden to the United States. The United States also as warned countries against granting Snowden political asylum.
It is unknown whether granting Snowden temporary asylum will affect President Obama's decision to attend a Group of 20 summit in Russia in September.