The deal is the second big military contract this year between France and Egypt, which Hollande said he increasingly views as a strategic partner.
"It was my preferred buyer because we already have military cooperation with Egypt," Hollande said of the deal he struck with President Abdel Fattah al-Sisi.
"Egypt plays an important role in the Middle East and wants to move towards a democratic transition, which is not easy, and we should support their efforts."
The two warships, which can each carry 16 helicopters, four landing craft and 13 tanks, were ordered by Russia in 2011 in a 1.2-billion-euro deal.
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France found itself in an awkward situation as the delivery date neared in 2014, with ties between Russia and the West plunging to Cold War lows over Moscow's annexation of Crimea and support for separatists in eastern Ukraine.
Paris faced the wrath of its allies around the world if it were to deliver the technology to Russia, and decided to cancel the delivery.
After months of intense negotiations, France and Russia agreed on the reimbursement of the deal in August.
Paris returned 949.7 million euros which had already been paid and also committed not to sell the two warships to a country that could "contravene Russia's interests", such as Poland or the Baltic states, a diplomatic source told AFP.
Several other countries were said to be interested in the warships, including Canada, India and Singapore.