Until the enforcement of the Lisbon Treaty the European Council was chaired by the country holding the rotating presidency of the European Union. It was decided that the Lisbon Treaty would change this so that the European Council had a permanent president to manage and coordinate the affairs of the European Council.
The President of the European Council is elected by the European Council on the basis of qualified majority voting for a two-and-a-half year period, renewable once. He/she is responsible for the preparation of the meetings, chairing them, drawing conclusions and following them up. Donald Tusk is the current President of the European Council. He has held the position since December 2014 and has been re-elected in March 2017.
According to the Lisbon Treaty, Article 15 paragraph 6:
The President of the European Council:
(a) shall chair it and drive forward its work;
(b) shall ensure the preparation and continuity of the work of the European Council in cooperation
with the President of the Commission, and on the basis of the work of the General Affairs Council;
(c) shall endeavour to facilitate cohesion and consensus within the European Council;
(d) shall present a report to the European Parliament after each of the meetings of the European Council.
(Consolidated versions of the Treaty on European Union and the Treaty on the Functioning of the European Union, 2010)
It is important to note that the President of the European Council is NOT the President of the EU; rather they are more like a chairman of the European Council as an institution. One cannot think of the President of the European Council as being like the President of the USA for example.
Please read the following link for more information on the work of the President of the European Council.
In the following sections, we shall see what the President does in practice and how the meetings of the European Council look like i.e. what happens before, during and after the meeting.