The whereabouts of Snowden - who is wanted by the United States after leaking details of vast US surveillance programmes - remained a mystery with his lawyer refusing to disclose the location for security reasons.
The White House said it was 'extremely disappointed' by Moscow's decision to grant Snowden asylum, adding that it would now review the need for a planned summit between President Barack Obama and President Vladimir Putin in September.
Nicknamed 'the invisible man' by journalists, the former National Security Agency (NSA) contractor on Thursday walked out of Moscow's Sheremetyevo airport unnoticed and took a taxi to a secret location. He now has temporary asylum in Russia for a year.
On Friday, the pro-Kremlin Life News website published a photograph showing Snowden smiling broadly as he walked through the airport arrivals area with a rucksack on his back and carrying another bag.
He was shown accompanied by his Russian lawyer Anatoly Kucherena and a staff member of WikiLeaks anti-secrecy website, Sarah Harrison, as well as an unidentified dark-haired woman.
Snowden and Harrison had stayed in the transit zone of the airport north of Moscow since flying in from Hong Kong on June 23.
Kucherena said Snowden would eventually emerge into public view and give interviews but that the fugitive first required an 'adaptation course' after so long in the transit zone.
'He has sorted out where he will live, everything is fine,' Kucherena told the RIA Novosti news agency Friday.
WikiLeaks said in a statement Snowden is now in a 'secure, confidential place'.
The founder of Russia's most popular social network VKontakte - 28-year-old Pavel Durov - offered Snowden a job as a programmer but Kucherena said he was still deciding what he would do.
Snowden thanked Russia and slammed the administration of US President Barack Obama for having 'no respect' for international or domestic law.
'But in the end the law is winning,' he said in the WikiLeaks statement.
'Negative influence on relations'
Russia's decision to award Snowden asylum status came two days after US soldier Bradley Manning was convicted of espionage for passing US secrets to WikiLeaks.
The White House warned Russia's decision could prompt Obama to cancel a planned visit to Moscow for talks with Putin ahead of the Saint Petersburg G20 summit.
'We're extremely disappointed,' White House spokesman Jay Carney told reporters. 'We're evaluating the utility of a summit in light of this.'
'This move by the Russian government undermines a long-standing record of law enforcement cooperation,' he added.
Obama himself declined to comment when pressed by reporters in an Oval Office briefing.
Putin has yet to comment on Snowden's temporary asylum. He was due to meet youth supporters at an annual summer camp later Friday.
On Friday the news anchor of Channel One television, seen as a Kremlin mouthpiece, said it was an 'open question whether the meeting of the two presidents will take place in Moscow in September'.
By granting asylum to Snowden, Russia has further strained already tense relations with the US, analysts said.
'The decision to grant Snowden asylum will in the short-term have a negative influence on Russia-US relations,' Foreign and Defence Policy Council think-tank chairman Fyodor Lukyanov told AFP.
Obama is likely to skip a Moscow visit but contacts between Russia and the US are already so limited that any sanctions by Washington would be largely symbolic, Lukyanov said.
Russian lawmakers backed Moscow's decision, saying it had no alternative but to give Snowden asylum.
'By cutting off the routes for him to fly out, the US left Moscow with no choice,' tweeted Alexei Pushkov, who heads the lower house of parliament's foreign affairs committee.
'Any other decision would have been a loss of face for Russia,' a lawmaker for ruling United Russia party, Vyacheslav Nikonov, who visited Snowden in the airport last month, told Kommersant daily.