In a resolution, EU lawmakers called on the bloc's 28 member states to grant protection to Snowden as a "human rights defender" after he blew the lid on the US government's mass surveillance programmes.
In a tweet, Snowden said the vote was "extraordinary."
"This is not a blow against the US government but an open hand extended by friends. It is a chance to move forward," he said in a second tweeted message.
Snowden has been living in exile in Russia since June 2013 and faces US charges of espionage and theft of state property which could put him in jail for 30 years.
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He says he was doing his duty as a citizen by informing others about the surveillance programmes which scooped up massive amounts of personal data in the name of national security.
Earlier this month, he hailed the top EU court's decision to strike down a transatlantic data deal used by companies like Facebook to send citizens' personal data to the US.