The former International Monetary Fund managing director will replace Mario Draghi, who has served as ECB president since 2011.
The European Council had already issued a formal recommendation for Lagarde, and Friday's move was just a confirmation after the European Parliament and the ECB also supported her.
The ECB sets monetary policy for the 19 countries that use the euro currency.
Lagarde will take office on Nov. 1 and will serve a non-renewable term of eight years.
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