The consortium will explore two sites off the western and northwestern shores of Crete. The areas cover 19,868 sq.km and 20,058 sq.km, respectively.
Greece launched the tender for the sites last year after expressions of interest by the consortium, in which Exxon and Total each have 40 percent. The group was the sole bidder.
The licences must be ratified by parliament before exploration work can begin.
Exxon and Total are currently exploring off Cyprus.
US Ambassador to Greece, Jeoffrey Pyatt hailed the decision by Greece, saying in a tweet that it is “big news” for Exxon Mobil.
— Geoffrey Pyatt (@USAmbGreece) July 3, 2018