WikiLeaks said it was escorting Snowden to Ecuador and had offered the support of its legal director Baltasar Garzon, a former Spanish judge known around the world for ordering the arrest of former Chilean dictator Augusto Pinochet.
Ecuador, which is already sheltering WikiLeaks' founder Julian Assange at its London embassy, confirmed Snowden has sought political asylum although foreign minister Ricardo Patino did not say whether the request had been accepted.
"The WikiLeaks legal team and I are interested in preserving Mr Snowden's rights and protecting him as a person," Garzon said in a statement. "What is being done to Mr Snowden and to Mr Julian Assange - for making or facilitating disclosures in the public interest - is an assault against the people."
Frustrating US attempts to extradite Snowden and put him on trial for the unauthorised release of secret surveillance files, WikiLeaks also sent one of its legal team to join him on a flight from Hong Kong to Moscow.
WikiLeaks said British legal researcher Sarah Harrison, one of Assange's closest advisers, had "courageously assisted Mr Snowden with his lawful departure from Hong Kong and ... in his passage to safety".
The campaign group gave no details about how it had helped to arrange the escape of one of the United States' most wanted men.
Advice came from Garzon, a high profile human rights campaigner who investigated corruption cases in Spain and opened an inquiry into alleged crimes under the right-wing dictatorship of General Francisco Franco, who died in 1975.
Since being kicked off the bench in Spain last year - when the Supreme Court found him guilty of illegal wiretapping in a political corruption case - he has spent most of his time outside Spain, advising on international law.
Garzon, who helped broker Assange's asylum in Ecuador's London embassy, was the dealmaker with Ecuador in the Snowden case, a source close to the WikiLeaks legal team told Reuters.
Another prominent legal figure who has represented Assange, the London-based barrister Geoffrey Robertson, was not directly involved in the Snowden case, the source added.
Before helping the former spy agency contractor - who leaked National Security Agency documents to a British newspaper - WikiLeaks was best known for publishing secret files, rather than giving direct support to those who leak them.
Assange has been in Ecuador's embassy in London since last June, seeking to avoid extradition to Sweden. It wants to question him about allegations of sexual assault and rape, which he denies.
British foreign secretary William Hague held talks with his Ecuadorean counterpart Patino last week in a failed attempt to find a breakthrough in a case that is becoming increasingly embarrassing for the London government.
Assange says he does not want to answer the allegations in person because he believes Sweden would hand him over to the US authorities, who would try him for his role in the release of 700,000 secret US files in one of the biggest leaks in American history.
In an interview with Reuters this month, Assange said he was encouraged by Snowden's actions. "In the United States, the ideals that I have fought for so long are now catching on, being embodied in the extraordinary courage of individuals such as Edward Snowden," he said.