Snowden slipped out of Moscow's Sheremetyevo airport on Thursday in a cloak-and-dagger operation overseen by his Russian lawyer, but unnoticed by the hordes of media trying to follow his every move.
The White House said it is "extremely disappointed" that the former National Security Agency (NSA) contractor was given asylum, and that it would now review plans for a US-Russia presidential summit in September.
Snowden, 30, is wanted on felony charges by the US after leaking sensational details of American surveillance programs, but Russia has refused to extradite him.
The fugitive was whisked away in a taxi at about 2pm local time, leaving his lawyer Anatoly Kucherena to reveal that he had received asylum in Russia for one year.
Kucherena, who helped Snowden make his asylum application on July 16, told AFP that Snowden's new place of residence would be kept secret for security "since he is the most pursued man on the planet".
The lawyer said Snowden would eventually give interviews to the press, but that he first requires an "adaptation course" after spending so long in the transit zone.
Unspecified "American friends" would assist him in Russia, Kucherena added.
Snowden has been staying in the transit zone of the Sheremetyevo airport north of Moscow since he flew in from Hong Kong on June 23. Until now, he had never formally crossed the Russian border.
The awarding of his asylum status came two days after US soldier Bradley Manning was convicted of espionage for leaking US secrets to WikiLeaks.
WikiLeaks, which has supported Snowden, said on Twitter that Snowden is still "under the care" of WikiLeaks British staffer Sarah Harrison, who flew in with him from Hong Kong and is believed to have been with him ever since.
VKontakte founder offers Snowden a job
The founder of Russia's most popular social network VKontakte offered a job to Edward Snowden on Thursday, after the US intelligence leaker left a Moscow airport with his new asylum papers.
"Today, Edward Snowden, the man who has exposed the crimes of American security services against the world's citizens, received temporary asylum in Russia," 28-year-old Pavel Durov, who co-founded the network in 2006, wrote on his VKontakte page.
"We invite Edward to Petersburg and will be happy if he decides to join the dream team of VKontakte programmers."
Durov's young age and sometimes extravagant statements have earned him comparisons with Facebook founder Mark Zuckerberg.
"No other internet company in Europe is more popular than VK," Durov said, referring to the shortened name of the social network, which boasts 210 million registered users and is based in Saint Petersburg.
"I think Edward would be interested in working on security of personal data of the millions of our users."