The 3 main institutions of the EU are each headed by a president:
Term: August 2014 - January 2017
Elected by: Members of the European Parliament
Term: December 2014 - May 2017
Appointed by: national leaders (heads of state or government of EU countries).
Term: November 2014 - October 2019
Appointed by: national leaders (heads of state or government of EU countries), with the approval of the European Parliament.
The Council of the EU - where national ministers discuss EU legislation - doesn't have a permanent, single-person president. Its work is led by the country holding the Council presidency, which rotates every 6 months. For example, representatives from the presidency country chair its meetings.