The vote was a formality after ambassadors on Monday backed the milestone agreement.
The majority of the bloc's energy ministers rubber-stamped the ban on Tuesday during a meeting in Brussels, with only Poland against. Bulgaria, Italy and Romania abstained.
The ban on internal combustion engines is a critical part of the bloc's push to be climate-neutral by 2050, with net-zero greenhouse gas emissions.
It was actually due to be approved earlier this month but Berlin frustrated its EU partners by withdrawing its support and demanding an exemption for synthetic fuels.
Germany's move was controversial since the deal had already passed under the traditional EU legislative process.
The fuels that Berlin sought exceptional rules for are still under development and must be produced using low-carbon electricity. Environmental activists oppose such fuels.
But manufacturers in Germany, one of the world's largest vehicle-producing nations, said the fuels could allow combustion engines to be used beyond 2035.
Critics said Germany's block was a result of domestic politics, with Chancellor Olaf Scholz under pressure to keep a coalition made up of his social democrats and rival Greens and liberals together.
His liberal partners wanted the exemption.
There was a breakthrough on Saturday after weeks of wrangling between the European Commission, the EU's executive arm, and the German transport ministry to resolve the row.
Vehicles with combustion engines can continue to be registered after 2035 if they only use fuels that are neutral in their CO2 emissions, German transport minister Volker Wissing said on Saturday.
"With the EU Council's final vote today the EU has taken an important step towards zero-emission mobility," the commission's climate chief Frans Timmermans tweeted.
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