The gas will be drilled from Israel's offshore natural gas fields, Tamar and Leviathan, Delek said in a statement to the Tel Aviv Stock Exchange.
Under the agreement, Delek and Noble Energy, which control the gas fields, will provide Egypt's Dolphinus Holdings Ltd. with about 64 billion cubic meters of natural gas from the two fields over a period of ten years.
Delek said it is looking into several options to transfer the gas to Egypt. The company is also considering going into negotiations with the East Mediterranean Gas Company, known also as EMG, an Israeli-Egyptian corporation.
Israeli Energy Minister Yuval Steinitz praised the economic and strategic implications of the agreement.
"The huge export deal forms Israel as a key player in the regional energy market and is expected to strengthen relations between the countries," he said in a statement.
In 2016, Delek and Noble signed agreements to supply natural gas from Tamar to a Jordanian chemical company in the Dead Sea.
Exports started in 2017. Under an additional contract, also signed in 2016, Israel would supply Jordan's electric company NEPCO with gas from Leviathan, starting from 2019.
Leviathan is a huge 622 billion cubic meters gas reservoir that was found off Israel's Mediterranean coast in 2010. The gas field is still under development with production expected to begin in 2019.
Gas production in Tamar, a nearby smaller gas field, kicked off in March 2013.
In December 2015, after years of political infighting, the Israeli government signed the long-awaited agreement allowing Noble and Delek Group to develop the Leviathan and Tamar gas fields while forcing them to sell two minor fields.