President Francois Hollande and Egypt's President Abdul Fattah al-Sisi "agreed on the principle and the terms of the acquisition", a statement said.
France halted the planned sale to Russia in late 2014, following the conflict in eastern Ukraine.
It has not divulged how much Egypt will pay for the warships, but Paris insists it is not out of pocket.
Differences over the cost had been reported during the French-Egyptian negotiations.
Russia agreed to buy the two warships - which can each carry 16 helicopters, four landing craft and 13 tanks - in a 2011 deal worth â‚¬1.2bn (Â£843m; $1.3bn).
Russia had paid about â‚¬840m in advance before the deal was stopped as the Ukrainian conflict erupted with Russia's annexation of Crimea.
After intense negotiations, Paris finally agreed in August to fully reimburse Russia, as well as foot the bill for training sailors and building port infrastructure in Vladivostok.
Egypt is fighting a long-running insurgency in its northern Sinai region.
That conflict intensified after the military overthrew Islamist President Mohammed Morsi in 2013.
The government has also launched an extensive crackdown on Islamist groups, including mass death sentences for members of Mr Morsi's Muslim Brotherhood.
This is only Egypt's latest purchase of military hardware from France.
Earlier this year, Egypt also bought 24 advanced Rafale fighter jets from France - prompting complaints from human rights groups that there was mounting evidence that Egypt had committed war crimes when it bombed Libyan targets.
There was scepticism over Wednesday's news of the deal from some on Twitter.
Egypt has agreed to buy two Mistral warships originally built for Russia, the French presidency has announced.