It leaves the Virgin Group with just one-fifth of the airline's equity. Delta will keep a 49 percent stake in Virgin Atlantic.
Talking about the deal, Sir Richard said, "This is a fantastic opportunity to extend our network and create a stronger customer champion, as well as being extremely beneficial to our people and the Virgin Atlantic brand that our customers love dearly."
The Virgin Atlantic president also wrote a letter to his staff, which read, "We've had to endure a consistently uneven playing field with British Airways keeping a stranglehold on Heathrow slots, enabling it to feed its long-haul operation from a myriad of short-haul flights across the UK and Europe."
Adding, "And now we have Brexit, which before it's even happened, has had a negative effect on the financial performance of both our holiday company and the airline, principally due to the collapse in the value of the pound."
Meanwhile, the chief executive of Air France-KLM, Jean-Marc Janaillac, shared, "With our partners Delta and Virgin Atlantic, we are pleased to reinforce our transatlantic partnership, offering our customers even more choice between Europe, UK and the United States via 12 hubs on both sides of the Atlantic."
Some further convoluted financial transactions are taking place as links between airlines deepen. Delta and the Shanghai-based airline, China Eastern, will each acquire a 10 percent holding in Air France-KLM, effectively by pumping in a total of 670m GBP.
The plan is likely to get the go-ahead early in 2019.