French Defence Minister Jean-Yves Le Drian will travel to Cairo on Monday to sign the contact with Egyptian President Abdel Fattah al-Sisi, a ministry source told AFP.
"The Rafale fighter jet has won its first export contract," French President Francois Hollande said in a statement issued by his office.
"The signing will take place in Cairo on February 16. I have asked the defence minister, Jean-Yves Le Drian, to sign on behalf of France," he added.
The military hardware would "allow Egypt to increase its security and assume its full role in the service of regional stability," Hollande said.
The Rafale jets are built by French manufacturer Dassault Aviation and have been used by the French air force in Libya and Mali.
France has also used the jets in Iraq as a part of the US-led fight against Islamic State militants.
Landing the contract will come as a relief to Dassault Aviation, which had yet to secure a single foreign sale after nearly three decades of development that cost tens of billions of euros.
Dassault Aviation has been locked in negotiations to sell 126 Rafale jets to India since 2012, without making much progress.
In another setback, France in 2013 failed to convince Brazil to buy its Rafale jets, losing out to Sweden's Saab in a multi-billion dollar contract.
Dassault chief executive Eric Trappier told Le Figaro daily last week that the company had "several prospects (for sales) in the Middle East which are very much live."
Talks are ongoing in Qatar and the United Arab Emirates among others.
He added that work continued on the "very complicated" India negotiations.
The French government initially agreed to buy 11 Rafales a year for its air force to help the programme. But in a bid to curb public spending it has since moved to scale back the number to only 26 planes over a six-year period.