Euronext came to life as the result of the merger of the Paris, Brussels and Amsterdam securities markets last year.
Financial analysts believe the purchase of Liffe will make Euronext a serious contender to become the lead exchange in Europe, if the integration process goes smoothly.
On completion of the deal, Euronext will move its derivatives business to London, which will operate on Liffe's Connect electronic trading platform. Liffe built and developed the platform, which it has sold to 450 sites across the world.
Euronext is still integrating the systems it acquired as a result of last year's merger. The group has been developing a single derivatives trading platform using its screen-based Next Derivatives System (NDS) that combines the systems of the Paris, Amsterdam and Brussels exchanges.
Euronext has also been working on a single clearing platform, based on its Clearnet Clearing 21 technology.
Commenting on the Liffe deal, Euronext said: "Euronext and Liffe will combine leading technology platforms for derivatives, cash and clearing operations, and generate potential growth opportunities for the focused future development and marketing of these and other technology platforms."