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."
French government sources said Egypt would pay 950 million euros ($1 billion) for the warships, with "significant" financing from Saudi Arabia.
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.
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.
It was an expensive decision for France, which has had to foot the bill of over one billion euros for the upkeep of the ships and the cost of training 400 Russian sailors to crew them.
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.
The defence ministry source who revealed the cost of the ships said they were due to be delivered to Egypt in March.The deal comes after Egypt became the first foreign buyers of France's Rafale fighter jet, agreeing to purchase 24 in February, in what Paris hailed as an "historic" accord.
The 5.2-billion-euro ($5.9 billion) sale of the planes and a frigate was a rare triumph for France which had failed to export its flagship multi-role combat jet.
However rights group Amnesty International slammed the decision to sell the planes to a nation it has accused of "alarming" human rights abuses.
Analysts said that deal required overlooking some serious abuses by a regime which Paris sees as a bulwark against several threats in the region.
With Libya to the west wracked by instability, and the threat from Islamic State-linked jihadists on its eastern flank, Egypt has become a strategic partner to France despite a rights record sullied by Sisi's brutal crackdown on opponents.
Sisi was elected president in May 2014 with almost 97 percent of the vote a year after toppling the country's first freely elected leader, Islamist Mohamed Morsi.
A subsequent crackdown on Morsi's supporters left at least 1,400 dead and thousands more in jail.
Hollande said during a visit to Egypt in August that the ever-closer ties between Paris and Cairo stemmed from the "fight against terrorism".
"Unfortunately it is the Egyptian people who pay the price," Didier Billion of the Paris-based Institute of Strategic and International Relations said at the time of the Rafale sale.
"We can shut our eyes over the rights situation in Egypt but we can't shut our eyes over Russia, because Russia is at the centre of an international power struggle," said Billion.
Sisi was also the subject of scathing global criticism over the detention and trial of Al-Jazeera journalists, two of whom he pardoned on Tuesday on the eve of a major Muslim holiday.