US firm Noble Energy, the lead partner, said in a statement that the contract signed Monday with the National Electric Power Company of Jordan (NEPCO) was for "300 million cubic feet per day over a 15-year term".
It includes an option to purchase a further 50 million cubic feet up to a total of 350 million daily.
"Gross contract revenues are estimated to be approximately $10 billion," it said.
Delivery to NEPCO is expected to begin at the same time as the estimated 22 trillion cubic foot field goes online to domestic clients in 2019 "subject to regulatory approvals from Israel and Jordan", Noble said.
Israel's government only ratified the consortium's plans for Leviathan on May 22, after long legal and political wrangling.
Noble is in partnership with Israeli energy firms Delek Drilling, Avner Oil Exploration and Ratio Oil Exploration.
"The signing of the export agreement between the Leviathan project and... NEPCO is an historic day and positions the Leviathan Project in the centre of the regional energy map," Delek Drilling and Avner CEO Yossi Abu said in a statement.
The project was previously blocked by Israel's supreme court as unconstitutional, with critics saying it gave overly favourable terms to the energy companies.
The agreement was then revised to reflect the court's objections and the government subsequently gave it the green light.
Leviathan is the largest of Israel's offshore gas fields, with enough reserves to turn the previously resource-poor country into a significant exporter.
"The partners in the Leviathan project will continue to pursue long-term agreements with other customers in the eastern Mediterranean, including in Egypt, Turkey and the Palestinian Authority," Abu said.
The consortium has already contracted to sell natural gas from the smaller Tamar field to the Jordan Bromine Company and the Arab Potash Company, starting "in late 2016", Noble's statement said.
The deal is likely to stir controversy in the kingdom. Although a peace treaty between the two countries signed in the 1990s ended the state of war, most Jordanians are opposed to normalising ties with Israel.
On Monday, a group calling itself the Campaign to Abort the Gas Deal With Israel calling for it to be repealed and stressing the need to boycott Israel.