Virgin Group and Sir Richard Branson will retain a 51% shareholding, and the Virgin brand will remain in place, the new partners said in a joint statement.
The deal is subject to regulatory approval in the US and Europe.
It follows a spat between Sir Richard Branson and Willie Walsh, boss of BA-owner International Airlines Group over the future of Virgin Atlantic.
Earlier, Willie Walsh offered to wager a “knee in the groin” in a bet with Sir Richard Branson over whether the Virgin brand would still be around in five years.
He was responding to a £1 million ($1.5 million) bet offered by Sir Richard Branson on Monday.
Virgin and Delta said the deal would allow them to “overcome slot constraints” and offer more flights from Heathrow.
The carriers will operate 31 peak-day round trips between the UK and North America.
“Our new partnership with Virgin Atlantic will strengthen both airlines and provide a more effective competitor between North America and the UK, particularly on the New York-London route,” said Delta boss Richard Anderson.
Sir Richard Branson said it was an “exciting day” in Virgin’s history.
“It signals the start of a new era of expansion, financial growth and many opportunities for our customers and our business.”
Singapore Airlines is selling its stake, which it has owned since 1999, because of increased competition in its local market.
Low-cost
airlines in particular have mushroomed, threatening more traditional carriers like Singapore Airlines.
Singapore Airlines has itself launched a low-cost carrier, called Scoot, and has been putting money into its regional service, SilkAir.
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