BRUSSELS — European Union legislators overwhelmingly approved a law on Thursday that puts about 130 of the euro zone’s largest banks under the direct scrutiny of the European Central Bank.

The legislation contains provisions that would give the European Parliament somewhat more oversight of a supervisory body, operating under the aegis of the central bank, when the body assumes its new authority. The vote is an important development, but not the final one, in a winding process that began in early 2012, during one of the most fevered periods in the euro zone financial crisis.

To take effect, the measure still needs approval from European Union governments, though that is expected to be a formality. The Single Supervisory Mechanism, the body it creates, is expected to start work during the autumn of 2014 after the European Central Bank conducts a “stress test” on the lenders coming within its purview.

The idea is that the central bank would do a better job than national supervisors of nipping financial problems in the bud so that governments would not need to resort to bank bailouts that destabilize the euro and penalize taxpayers. Once up and running, the new supervisory authority will have a range of powers to intervene when it detects problems, including the ability to conduct inspections that could lead to sanctions on banks or their managers.