The former US security contractor has received refugee status in Russia and has been granted a year’s asylum, his lawyer Anatoly Kucherena said.
Mr Kucherena told local reporters he had passed Edward Snowden documents from Russia’s Federal Migration Service. He added: “I have just seen him off. He has left for a secure location … Security is a very serious matter for him.”
After weeks staying out of sight from hordes of reporters desperate for a glimpse of him, Mr Snowden managed to slip away in a taxi without being spotted.
“He is the most wanted man on planet earth. What do you think he is going to do? He has to think about his personal security. I cannot tell you where he is going,” Mr Kucherena said.
He added: “He can live wherever he wants in Russia. It’s his personal choice.”
The US wants him sent home to face prosecution for espionage after he leaked classified information while working for the National Security Agency (NSA).
Mr Snowden, who alleges that the NSA has been involved in widespread eavesdropping on phone calls and email messages, flew into Moscow’s Sheremetyevo airport from Hong Kong on 23 June.
He has remained in the airport’s transit area since then. He had hoped to fly to Latin America, where three countries have offered to shelter him, but was concerned that the United States would prevent him reaching his destination.
Mr Snowden’s case has caused new strains in relations between Russia and the US which wants him extradited to face espionage charges.
The White House has signalled that President Barack Obama could consider boycotting a planned summit with Russian President Vladimir Putin in Moscow in early September.
But a senior Kremlin official said ties between Russia and the United States would not suffer because of what he said was a “relatively insignificant” case.
“Our president has … expressed hope many times that this will not affect the character of our relations,” Yuri Ushakov, Mr Putin’s top foreign policy adviser, said.
He said there was no sign that Mr Obama would cancel the planned visit in September.