The highest body of the Institute is the Membership, which elects from among its Fellows the main governing body: the Council.

The Council is made up of up to 56 elected Individual Fellows as well as ex-officio members representing selected institutions. In addition, the President, the two Vice-Presidents and the Treasurer become ex-officio members of the Council from the moment they take office. Council elections for half of the seats take place every two years at the Membership meeting. The Council delegates many of its tasks and powers to its Standing committees which deal with matters such as Membership and fundraising issues. The Council elects from among its members an Executive Committee, the Association's administrative body.

Furthermore, there is a Senate in place to provide advice, which appoints from among its members an Arbitral Tribunal, tasked with settling any disputes within the Association.

Outside the formal bodies is ELI's Scientific Director, who has oversight of projects, and ELI's Secretariat, which is tasked to support the competent bodies of the Institute.