Formal agreement to make the European Central Bank the "single supervisor" for big banks was agreed by 556 votes in favour and 54 against.
The step, the first pillar in a wider scheme towards safer and more accountable banking, was broadly agreed in March by members of the 17-nation eurozone and Parliament but had not been put to the vote.
In Riga, ECB president Mario Dragi said he welcomed the vote on what would be called the Single Supervisory Mechanism (SSM).
MEPs had postponed this week's vote by 48 hours, demanding more transparency and control, including a say in approving the chair and vice-chair of the supervisory board and the possibility of launching probes into possible errors.
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Among other changes to the original plan is the possibility for non-eurozone nations to join as well as the strict division of ECB staff between monetary policy and supervision.
Individual MEPs will also be able to question the supervisor in writing and receive a rapid reply.
"Now our attention must turn urgently to the Single Resolution Mechanism," he said, referring to the second pillar in the scheme for a single banking union.
The resolution mechanism would give the Commission the power to shut down any of the eurozone's 6,000-plus banks even if national authorities disagreed.
Banking union in effect would shift the burden of dealing with failing banks from taxpayers with new rules forcing creditors to take losses and a resolution fund created through mandatory levies on the banks.
The EU's Internal Markets Commissioner Michel Barnier said that "with this key piece of legislation, we are not only strengthening our banks and the financial stability of the eurozone, we are also strengthening economic integration."
Saying it will be five years this week since Lehman Brothers filed for bankruptcy, triggering the biggest global financial crisis in modern history, Barnier said the supervisory mechanism was an essential part of "rules to better protect European citizens and to prevent future crises.