Delek said in a statement the deal will close within two business days. It did not name the buyer.
Delek will make a profit of 116 million shekels (£23.3 million) from the sale, of which 73 million shekels will be recorded in its 2018 financial results and the rest in 2017.
Faroe is an oil and gas exploration and production company operating in the North Sea.
Reporting by Tova Cohen, reporting by Louise Heavens