The European Parliament has voted overwhelmingly in favour of the new 27-strong team of European commissioners.
Each commissioner had previously faced a hearing in the European Parliament.
The Commission is the EU's executive arm, responsible for drafting EU laws and ensuring that the 27 member states comply with the EU treaties.
Bulgaria's first nominee, Rumiana Jeleva, failed to convince MEPs about her suitability for the job, so she was replaced by Kristalina Georgieva.
MEPs cast 488 votes in favour of the Commission, 137 against and there were 72 abstentions.
The parliament's vote on the whole Commission was delayed by three months because ratification of the Lisbon Treaty was not completed until November.
The president of the Commission, veteran Portuguese conservative Jose Manuel Barroso, had already been approved for a second term by the EU government leaders, before Tuesday's vote in Strasbourg.
The new line-up includes the UK's Baroness Ashton, the EU's High Representative for Foreign Affairs. The new post, created by the Lisbon Treaty, also makes her a Commission vice-president.
MEPs cannot vote on individual commissioners - only on the whole Commission team. But they can force changes in its composition by rejecting the whole team. That happened in 2004, when Italy withdrew its commissioner-designate for justice, Rocco Buttiglione. MEPs disliked his opposition to gay rights and conservative attitude towards women.
Under the Lisbon Treaty the MEPs' legislative powers have been expanded. It puts them on an equal footing with the Council - the grouping of member states' governments - for most legislation, including the budget and agriculture.
On Tuesday the parliament approved new principles of co-operation with the Commission.
The new rules include equal treatment for the parliament and the Council regarding access to the Commission's meetings with national experts.
There will be a new Question Hour with commissioners at the parliament's monthly plenary week in Strasbourg.
If the parliament asks Mr Barroso to withdraw his confidence in a commissioner, "he must seriously consider whether to require the resignation of the commissioner or explain his refusal to do so before parliament in the following plenary session," the parliament's press service says.
The leader of the UK Conservatives in the parliament, Timothy Kirkhope MEP, called for an annual assessment of the Commission by the parliament.
The European Conservatives and Reformists - the grouping led by the Conservatives - abstained in the vote, after Mr Kirkhope called it "a flawed process".
He said some of Mr Barroso's team were "mediocre and made a poor impression".
The leader of the liberal group ALDE, Belgian MEP Guy Verhofstadt, urged the new Commission to be "bolder, more ambitious" in areas such as economic and social policy, climate change and foreign policy.
The Socialist (S&D group) leader, Martin Schulz MEP, stressed that the EU's method of "permanent compromise" was "better than ideological conflict".
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