Virgin Atlantic expects a deal for Air France-KLM to buy a stake in the British airline from Richard Branson's Virgin Group to complete in early 2019, its chief executive said.

Virgin Group said last July it would sell a 31 percent stake in Virgin Atlantic to Air France-KLM, reducing its stake to 20 percent, and leaving U.S. carrier Delta DA.L as the largest shareholder with a 49 percent stake.

Craig Kreeger, the chief executive of Virgin Atlantic, said that the groups were applying for anti-trust approval in the United States, something he was confident they would be granted, in a process that he thought would take a year.

"Our expectation is this is an early 2019 launch of the expanded joint venture," he said at an event on Wednesday.