The deal is valued at around £220 million and is part of an expanded transatlantic joint venture with Delta Air Lines.
Virgin Group will retain a 20 per cent stake and chairmanship of the UK long-haul carrier founded by Sir Richard Branson.
At the same time, Delta will retain its 49 per cent shareholding.
The long-planned arrangement is designed to expand and strengthen the three airlines’ transatlantic joint-venture.
Air France-KLM, Delta and Virgin Atlantic will now co-ordinate efforts to secure the appropriate regulatory approvals.
The move comes as traditional carriers on Prime North Atlantic routes, including rival partners British Airways and American Airlines, face increasing competition from low cost newcomers such as Norwegian, Wow Air and Primera Air together with the leisure airlines of Tui and Thomas Cook.
“The airlines’ expanded joint venture will become the preferred choice for customers travelling across the Atlantic offering the most comprehensive route network, convenient flight schedules, competitive fares and reciprocal frequent flyer benefits, including the ability to earn and redeem miles across all carriers,” explained a joint statement.
“Customers will also benefit from the co-location of facilities at key hub airports to improve connectivity and access to each carrier’s airport lounges for premium passengers.”
Also today, Air France-KLM has appointed finance chief Frederic Gagey as interim chief executive.
The move follows the resignation of chief executive Jean-Marc Janaillac amid repeated strikes.
Gagey will be part of a management committee of three that will take decisions during the transition period.
Board member Anne-Marie Couderc will act as non-executive chairwoman during that time.
Members of the board expressed their “deep regret over the successive strikes” affecting Air France in recent weeks, adding they had a “negative impact on the group’s financial results”.
Workers have held 13 days of strikes since February, disrupting air traffic.