The vote paves the way for Snowden to give evidence through a pre-recorded video message in response to questions asked in advance by MEPs.
The evidence session is expected to be held in the coming weeks, possibly during the week starting on Monday 20 January.
British MEPs were strongly opposed to Snowden's testimony, with one UK Conservative, Timothy Kirkhope, describing him as a "traitor" and “criminal”.
Other MEPs seemed to disagree, however, and voted overwhelmingly in favour of the motion, with 36 in favour, 2 against and 1 abstention.
Dutch Liberal MEP Sophie in 't Veld, vice-chair of the civil liberties committee, said that the video testimony would provide “an opportunity to give citizens across Europe the answers they deserve over mass surveillance”.
“I would also like to ask Snowden why he felt the legal avenues to report abuse were not open to him and whether he believes whistle-blowing procedures have now been improved,” she said.
According to in 't Veld, some MEPs were concerned that Snowden’s testimony could derail the ongoing trade talks with the US (see background).
“But if anything it is the other way round. The truth is that unless we receive proper answers over mass surveillance and assurances on data protection it will be difficult for any trade deal to be completed,” the Dutch liberal MEP stressed.
During a debate with European bloggers held on Tuesday, Viviane Reding, the European Commission vice-president in charge of justice and fundamental rights, publicly thanked Snowden for making his revelations.
When Snowden’s revelations were made public, Reding said: ‘Thank you Mr Snowden’, because she said she had until then the greatest difficulty to raise the issue, even within EU institutions.