Backing the draft were traditional media, in urgent search of revenue at a time when web users shun newspapers and TV and advertising revenue is syphoned away by online platforms.
MEPs meeting in the French city of Strasbourg voted 438 in favour of the measure, 226 against, with 39 abstentions.
European lawmakers were sharply divided on the issue, with both sides engaging in one of the biggest rounds of lobbying that the EU has ever seen.
MEPs settled on a text that compromised on some of the ways news organisation will be able to charge web companies for links to content.
It also slightly watered down a proposal for so-called upload filters that will force platforms - such as YouTube or Facebook - to automatically delete content that violates copyright.
The vote in the European Parliament "is a strong and positive signal and an essential step to achieving our common objective of modernising the copyright rules in the European Union," said EU commissioners Andrus Ansip and Mariya Gabriel, who had proposed the reform.
Before the vote, French President Emmanuel Macron had called it "a fundamental battle for copyright", adding that "Europe must be worthy of its culture".
The draft had been fiercely resisted by US tech giants as well as online freedom activists, with some campaigners warning it could spell the end of viral "memes" or jokes.
They also fear that automatic filters to prevent users sharing content subject to copyright could be misused to censor political messages or other forms of free expression.
With the vote, MEPs can now start negotiations with the European Council representing the 28 member states which already reached a compromise on the issue in May.
These closed-door discussions, which also include the European Commission, are known in EU jargon as "trilogues" and can take several months before any compromise is put to a fresh vote.