It is not yet clear how the gas from both fields will be transported to Egypt. Delek Group, which controls Delek Drilling, said a number of options were being considered, including connecting Egypt to Israel's own transmission network and using the pipelines to the east Mediterranean and Jordan.
The deal, reportedly worth 15 billion Dollars, has been signed between Delek Drilling and its USA partner Noble Energy Inc. on the one side, and the Egyptian company Dolphinus Holdings Ltd.
The deal with Egypt only became possible after the country's leaders changed regulations, allowing private companies to import gas.
Egypt was once a net exporter of gas, but years of political instability and mismanagement, including deals which MEE has investigated, left it to import gas for its rising population.
At the end of 2016, Israel also gave the green light to sell two gas fields, estimated to hold reserves of around 60 billion cubic metres, to the Greek company Energean.
Israel prevents the Palestinian Authority from drilling in the gas fields located in Palestine's territorial waters off the Gaza coast.
An Egyptian government official who declined to be identified said the deal did not mean Egypt itself would import any gas from overseas.
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Tamar is already producing natural gas, and the Leviathan field is expected to start late next year.
Meanwhile, MP Abdel Hamied Kamal said in a statement that he presented an official petition to the House of Representatives which called upon parliament to recall Egypt's Petroleum Minister Tarek El-Molla for discussion over the deal with Israel. These agreements, one for natural gas from Leviathan and one for Tamar, each provide for total contract quantities of 1.15 trillion cubic feet of natural gas.
Dallas-based Zion Oil & Gas is also involved in Israel's quest for fossil fuel wealth. The security cooperation between Egypt and Israel has strengthened since president al-Sisi assumed power in 2014, and the diplomatic cooperation has boosted.
Israeli gas companies' shares rose the most in nine years on Monday.
Both Israel and Egypt still need to provide regulatory and government approvals for the exports. However, they are looking at using a pipeline that previously.
They are joined in Tamar by Isramco Negev, Tamar Petroleum - a spin-off of Delek - and two other small partners.