Shemen plans to drill in relatively shallow water 16 km off the coast of Ashdod, a major port that is also home to a naval base and one of Israel's two oil refineries.
Shares in Shemen were up 17% in midday trade in Tel Aviv on Monday.
Consulting firm Netherland and Sewell Associates estimated there is the potential for 227 million barrels of oil and 3 trillion cubic feet of natural gas in the Shemen 387 license.
Shemen, whose chairman is former IDF Chief of Staff Gabi Ashkenazi, estimated the cost of the drill at $98 million.
Negotiations with the military lasted nearly a year.
Avi Bnayahu, who was previously the top spokesman for Israel's armed forces and is a strategic adviser to Shemen, said there are military activities in the area of the drill that required defense approval.
"In the past there was a phenomenon that to any request to carry out economic or civilian initiatives the armed forces would say 'Not in my backyard.' In recent years the military has sought a path of compromise," he told Reuters.
Shemen said it had signed an agreement with Atwood for leasing the Atwood Beacon rig.
Israel currently imports nearly all of its crude oil, mainly from Russia.
Shay Salinas contributed to the report