The security cabinet approved the deal seven to three after four and a half hours of debate, giving it final Israeli government approval, a spokesman said.
Prime Minister Benjamin Netanyahu and others have promoted its economic benefits, with talk of building a pipeline to Turkey to export Israeli gas, and the need to find allies in the turbulent Middle East.
But there have been objections over Israel agreeing to pay USD 20 million in compensation to families of the Turkish activists killed in the raid.
Turkey will be allowed to deliver aid to Palestinians in Gaza as part of the deal, but Netanyahu has stressed that Israel's blockade on the enclave will remain in place.
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Turkey has been seeking to restore its clout in the region after a diplomatic crisis with Russia and other foreign policy difficulties.
Ankara said yesterday that the two countries would begin the process of exchanging ambassadors this week. It was unclear if last night's attack at Istanbul airport that killed 41 people would affect the process.
Nine activists aboard the Turkish-owned Mavi Marmara ferry were killed, with a 10th person later dying of his wounds.