President François Hollande and Egyptian President Abdel Fattah al-Sisi "have agreed on the principle and terms and conditions of Egypt's acquisition of the two Mistral class vessels," the statement from the French president's office said.
The deal comes a little over six weeks after France and Russia reached an agreement to fully reimburse Moscow for the scrapped €1.2-billion ($1.3-billion) deal.
The first Mistral had been due for delivery in 2014, while the second was to be delivered this year.
But as Russia and the West became embroiled in their worst standoff since the Cold War over the Ukraine crisis, France's partners said delivering the ships would undermine their efforts to isolate Moscow over its 2014 annexation of Crimea and support of separatists in eastern Ukraine.
The sale to Egypt of the vessels will come as a huge relief to the French government which was faced with the prospect of some very expensive military hardware rusting away at the western French port at St Nazaire.
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 eight 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.
(France faced protesters when it looked like the deal was to go ahead. Photo: AFP)
France 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 countries were said to be interested in the warships, including Canada, India and Singapore.
It has not been divulged how much Egypt will pay for the warships.
While experts have said any sale would likely see a significant price cut, government spokesman Stephane Le Foll said there would be no "loss" of money in the new accord.
The deal between Egypt and France is their second big military contract this year after Egypt became the first buyers of the Rafale fighter jet, agreeing to purchase 24 in February.
The 5.2-billion-euro ($5.9 billion) sale of the planes 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 jets 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 stable partner in a chaotic 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 al-Sisi's brutal crackdown on opponents.
Sisi was elected president in May 2014 with 96.91 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