The contract, a firm order for 34 Rafales and an option on 12 more, is worth 6.3 billion euros the French presidency said with "great satisfaction" on Thursday.
It is to be signed on 4 May in Doha in the presence of President François Hollande.
The Emir of Qatar finally gave the go-ahead for the deal during a visit to Doha by French Defence Minister Jean-Yves Le Drian on 21 April, his 10th such mission since 2012.
The Rafale has been the French air force's jet fighter since 2004 but six of Dassault's efforts to sell it abroad have fallen through and negotiations to sell 126 to India dragged on for years.
But things have looked up this year.
Talks with the United Arab Emirates are moving "in the right direction", according to Foreign Affairs Minister Laurent Fabius, and Malaysia is soon to invite tenders for 16 planes.