Snowden's whereabouts will be kept a secret for security reasons, lawyer Anatoly Kucherena said, making it even harder to keep track of the former NSA systems analyst, who has been largely hiding out at Moscow's Sheremetyevo airport since his arrival from Hong Kong on June 23.
The U.S. has demanded that Russia send Snowden home to face prosecution for espionage over his leaks that revealed wide U.S. Internet surveillance practices, but Russian President Vladimir Putin dismissed the request. In a statement released by the WikiLeaks secret-spilling site, Snowden thanked Russia and lashed out at the Obama administration.
"Over the past eight weeks we have seen the Obama administration show no respect for international or domestic law, but in the end the law is winning," he said. "I thank the Russian Federation for granting me asylum in accordance with its laws and international obligations."
The move could further strain U.S.-Russian relations already tense amid differences over Syria, U.S. criticism of Russia's human rights record and other disputes. Putin has said his asylum was contingent on him not hurting U.S. interests, but the Kremlin could have interpreted that to exclude documents he had already leaked to newspapers that continue to trickle out.
In his application for asylum, Snowden said he feared he could face torture or capital punishment if he is returned to the U.S., though the U.S. has promised Russia that is not the case. The U.S. has revoked his passport, and the logistics of him reaching other countries that have offered him asylum, including Venezuela, Nicaragua and Bolivia, are complicated.
"He now is one of the most sought after men in the world," Kucherena told reporters at the airport. "The issue of security is very important for him."
The Guardian newspaper on Wednesday published a new report on U.S. intelligence-gathering based on information from Snowden, but Kucherena said the material was provided before Snowden promised to stop leaking.
The one-year asylum can be extended indefinitely, and Snowden also has the right to seek Russian citizenship. According to the rules set by the Russian government, a person who has temporary asylum would lose it if he travels abroad.
Kucherena said it would be up to Snowden to decide whether to travel to any foreign destination, but added that "he now has no such plans."
Snowden's father said in remarks broadcast Wednesday on Russian television that he would like to visit his son. Kucherena said he is arranging the trip.
WikiLeaks, which has adopted Snowden's cause, said in its statement that legal adviser Sarah Harrison has been with him in the transit zone for 39 days and remains with him. It said only that they left the airport in a taxi and that they are heading to a "secure, confidential place."
The group also praised Russia for providing him shelter.
"We would like to thank the Russian people and all those others who have helped to protect Mr. Snowden," WikiLeaks said on Twitter. "We have won the battle - now the war."
Kucherena said that Snowden spent little time packing. The lawyer said the fugitive had friends in Russia, including some Americans, who could help ensure his security, but wouldn't elaborate.
"He has got friends, including on Russian territory, American friends, who would be able to ensure his safety for the time being," Kucherena said.
He refused to say whether Snowden would stay in Moscow or move to stay elsewhere in Russia, saying the fugitive would discuss the issue with his family.
Kucherena argued that Russia did the right thing by offering shelter to Snowden despite U.S. pressure. "Russia has fulfilled a humanitarian mission with regard to the U.S. citizen who has found himself in a difficult situation," he said, voicing hope that the U.S. wouldn't try to slam Russia with sanctions.
Putin's foreign affairs aide, Yuri Ushakov, sought Thursday to downplay the impact on relations between the two countries.
"This issue isn't significant enough to have an impact on political relations," he said in remarks carried by Russian news agencies.
He said that the Kremlin hasn't heard any signal from Washington that Obama could cancel his visit to Moscow ahead of next month's G-20 summit in St. Petersburg.
But Sen. Robert Menendez, Chairman of the Senate Foreign Relations Committee, said in a statement that the Russian decision to grant asylum to Snowden would hurt ties.
"Edward Snowden is a fugitive who belongs in a United States courtroom, not a free man deserving of asylum in Russia," the Democratic lawmaker said. "Regardless of the fact that Russia is granting asylum for one year, this action is a setback to U.S.-Russia relations. Edward Snowden will potentially do great damage to U.S. national security interests and the information he is leaking could aid terrorists and others around the world who want to do real harm to our country."
Lyudmila Alexeyeva, a veteran of Russia's human rights movement and head of the respected Moscow Helsinki Group, welcomed the news on asylum for Snowden, but added that his quest for freedom of information has landed him in a country that has little respect for that and other freedoms.
"Having fought for the freedom and rights, Snowden has ended up in a country that cracks down on them," Alexeyeva said, according to the Interfax news agency.
Rachel Denber of Human Rights Watch sounded a similar note. "He cannot but be aware of the unprecedented crackdown on human rights that the government has unleashed in the past 15 months," Denber said in an e-mailed comment.
Putin has launched a wide-ranging crackdown on dissent since his inauguration for a third presidential term in May 2012, with the Kremlin-controlled parliament stamping a series of laws that introduced heavy fines for participants in unsanctioned protests, imposed new tough restrictions on non-government organizations.
A law passed in June bans imposes hefty fines for providing information about the gay community to minors or holding gay pride rallies, a move that has prompted gays in the U.S. and elsewhere to call for boycott of the 2014 Winter Olympics in Sochi.
Laura Mills contributed to this report.