From the IEA's Treaty of Lisbon 2007: Consolidated Treaties version:

Article 14
1. The European Parliament shall, jointly with the Council, exercise legislative and budgetary functions. It shall exercise functions of political control and consultation as laid down in the Treaties. It shall elect the President of the Commission.

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4. The European Parliament shall elect its President and its officers from among its members.

The procedure is spelled out more fully in a later article:

Article 17

Taking into account the elections to the European Parliament and after having held the appropriate consultations, the European Council, acting by a qualified majority, shall propose to the European Parliament a candidate for President of the Commission. This candidate shall be elected by the European Parliament by a majority of its component members. If he does not obtain the required majority, the European Council, acting by a qualified majority, shall within one month propose a new candidate who shall be elected by the European Parliament following the same procedure.

The Council, by common accord with the President-elect, shall adopt the list of the other persons whom it proposes for appointment as members of the Commission. They shall be selected, on the basis of the suggestions made by Member States, in accordance with the criteria set out in paragraph 3, second subparagraph, and paragraph 5, second subparagraph.

The President, the High Representative of the Union for Foreign Affairs and Security Policy and the other members of the Commission shall be subject as a body to a vote of consent by the European Parliament. On the basis of this consent the Commission shall be appointed by the European Council, acting by a qualified majority.

8. The Commission, as a body, shall be responsible to the European Parliament. In accordance with Article 234 of the Treaty on the Functioning of the European Union, the European Parliament may vote on a motion of censure of the Commission. If such a motion is carried, the members of the Commission shall resign as a body and the High Representative of the Union for Foreign Affairs and Security Policy shall resign from the duties that he carries out in the Commission.

So, the President of the Commission requires a qualified majority of the Council and a majority of the Parliament. The same is then true of the rest of the Commission including the HRCFSP who will be nominated by the Council and the President of the Commission jointly.

The President of the European Council is not subject to any control by any other body. As such, he is more analogous to the President of the Parliament and should be a mostly ceremonial and procedural position. Executive and representational powers should be strictly limited to the Commission President and the HRCFSP, who are approved by all the European institutions and subject to Parliamentary control.

We have met the enemy, and he is us — Pogo