(CNN) -- National Security Agency leaker Edward Snowden's application for political asylum has been approved, and he has left a Moscow airport, Russian lawyer Anatoly Kucherena told CNN on Thursday.

Snowden has legal status in Russia for one year, Kucherena said, but the attorney would not disclose his location, citing security reasons.

"We would like to thank the Russian people and all those others who have helped to protect Mr. Snowden. We have won the battle -- now the war," WikiLeaks tweeted when the news hit.

In another tweet, the group said, "Edward Snowden was granted temporary asylum in Russia for a year and has now left Moscow airport under the care of WikiLeaks' Sarah Harrison."

And another tweet: "FLASH: We can now confirm that Edward Snowden's welfare has been continuously monitored by WikiLeaks staff since his presence in Hong Kong."

The Russian government "has been signaling ... for some time" that it planned to grant Snowden temporary asylum, a U.S. official tells CNN, saying, "I don't think it's a shock." While the Russians have signaled their intentions publicly, the U.S. also learned of the country's plans in private conversations between senior U.S. and Russian officials over the last several weeks, the official added.

Senior White House, Justice Department, State Department and CIA officials had been speaking privately with their counterparts in Russia since the crisis developed. The official did not, however, say that the U.S. had been formally notified of the decision in advance.

While the Obama administration has to make a decision about what to do next in its relations with Moscow, the U.S. national security agencies are hoping to continue cooperation with Russia on counterterrorism matters. The official said the April Boston terror attack "reinforced the need for that."

The U.S. and Russia also are already cooperating on security for the 2014 Sochi Olympic Games, which the official noted is already being threatened by Chechen terrorists.

Snowden's father's lawyer talks

On Wednesday night, a lawyer representing Lon Snowden, Edward Snowden's father, appeared on "Anderson Cooper 360" and said that Snowden was in good health in Russia and that his lawyer was open to hammering out an ending that would satisfy all.

Attorney Bruce Fein relayed the conversation he had with Kucherena.

"There may be a time where it would be constructive to try and meet and see whether there can't be common ground that everyone agrees would advance the interest, the United States, Mr. Snowden, Lon, his father, and the interest of Russia in trying to resolve this in a way that honors due process and the highest principles of fairness and civilization," Fein said.

Kucherena earlier told Russian news agency Itar-Tass that he'd start working on Lon Snowden's visa application.

"I telephoned him (Edward Snowden) today. We agreed that I would prepare an invitation for his father to visit Russia. I hope that the visa formalities will not be long," Kucherena said Wednesday.

Snowden has said he is afraid he would not get a fair trial if he came back to the United States.

Snowden leaks again

On Wednesday, Snowden once again made himself a thorn in the side of the NSA.

The British daily The Guardian, which broke news of the NSA programs on the surveillance of phone and Internet metadata after Snowden leaked the information, revealed yet another NSA data collecting scheme.

The report says that according to the leaked documents, XKeyscore allows intelligence agents to see anything you've ever done on the Internet. With ease, they can observe your browsing history, searches, e-mails, chats and more, the report says, and it does not require a search warrant.

After the article was published, Snowden came forward as the source.

FBI and Snowden's father

Snowden's father told Anderson Cooper that the FBI had wanted to fly him to Moscow to encourage the National Security Agency leaker to come home to the United States.

But Lon Snowden said he backed out because it was not clear he would be able to speak to his son.

When he asked FBI agents if they would be able to set up communications, they hesitated, he said. It made him suspicious.

"I'm not going to get on a flight and go to Moscow and sit on a tarmac to be an emotional tool for you to use against him. I want to first be able to speak to my son," he told them.

Lon Snowden has said that he wants his son to stay in Russia until he is confident he can get a fair trial in the United States.

"I am not confident at all," he said.

The multiple guilty verdicts handed to leaker Pfc. Bradley Manning increased his unease, although he says his son's case is "completely different."

"I think my son has exercised discretion in the information that he has shared," he said.

By the numbers

Russian citizens generally support the NSA leaker.

An opinion survey reported by RIA Novosti shows 51% of Russians back Edward Snowden's actions. The rest either disapprove or haven't made up their minds yet.

On the question of asylum, 43% are generally in favor of the idea, according to the Levada Center poll.

Snowden patriotic?

A former employee of a government contractor, Snowden leaked to the media that the NSA had secretly collected and stored millions of phone records from accounts in the United States. It also collected information from U.S. companies on the Internet activity of overseas residents, he said.

Lawmakers in Washington have built a criminal case against him.

Fein has objected to the government's intent to prosecute Snowden.

"The majority of the American people now have voiced grave concerns about the scope of that program. And it seems somewhat odd to be prosecuting somebody for disclosing government wrongdoing."

He said that Snowden had the courage to spark a conversation that President Barack Obama has called "urgent."

CNN's Barbara Starr contributed to this report.