The agreement, which was announced on Thursday and is expected to face a parliamentary vote, aims to end months of uncertainty and set a framework for the exploitation of gas discoveries.
It is expected to raise major new government revenues and could provide Israel with strategic leverage in the region if it becomes a gas exporter.
"This money will benefit education, health, social welfare and other national needs," Prime Minister Benjamin Netanyahu said ahead of the cabinet vote, which passed 17-1.
They have also teamed up to develop the offshore Leviathan field, considered to be the largest in the Mediterranean.
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The agreement stipulates that Delek sells its 31 percent share of Tamar within six years, and Noble decrease its holdings there from 36 to 25 percent to no longer be the largest shareholder.
It also contains amendments to an earlier version, such as linking the price of gas to an energy index, which is meant to lower costs for consumers.
The consortium committed to invest USD 1.5 billion to develop the Leviathan field over the next two years.
The talks have been controversial, with many fearing the deal would overly favour the companies involved.
The agreement notes that Israel's anti-trust authority objects to it on the grounds that it does not allow for sufficient competition.
To circumvent that obstacle, Netanyahu's inner cabinet in June declared gas production to be linked to national security, thus allowing the government to override laws related to monopolies.
Netanyahu has pushed hard to speed up gas production in the Mediterranean, drawing criticism from political opponents who accuse him of not ensuring sufficient benefits for the public in the negotiations.
Dov Khenin, a lawmaker from the Joint List, was one of the opposition members to speak out against the agreement, listing a series of reasons why it was tantamount to a "concession agreement" to Noble and Delek.