The announcement comes after it was speculated that Alaska Airlines was understood to be making for Virgin America.
An offer of $55 per share had been expected. The deal values Virgin America at $2.6bn.
Including existing Virgin America indebtedness and capitalised aircraft operating leases, the aggregate transaction value is approximately $4bn, Alaska Air said.
Alaska Air's bid of $57 per share in cash is a premium of near 47 percent against Virgin America's Friday close.
David Cush, Virgin America president said: "Our mission has always been to create an airline that people love – and we accomplished that while changing the industry for the better. Joining forces with Alaska Airlines will ensure that our mission lives on, and that the stronger, combined company will continue to be a great place to work and an airline that focuses on an outstanding travel experience."
Meanwhile, Alaska Air's chief executive Brad Tilden said the deal brings together two "incredible groups of employees to build on the successes they have achieved as stand-alone companies to make us an even stronger competitor nationally."
In a somewhat emotional farewell, Sir Richard Branson said: "Our US airline, Virgin America, also started out of frustration. As more airlines consolidated and grew larger and more focused on the bottom line, flying in the US became an awful experience. Despite moves to block our airline from flying, Virgin America began service in August 2007 - with the goal of making flying good again."
"The airline has also done something almost inconceivable in the airline industry: Virgin America won the hearts and fierce loyalty of consumers around the country. People love this airline.
"I would be lying if I didn’t admit sadness that our wonderful airline is merging with another. Because I'm not American, the US Department of Transportation stipulated I take some of my shares in Virgin America as non-voting shares, reducing my influence over any takeover. So there was sadly nothing I could do to stop it."
Virgin America's share price shot up over 33 per cent in pre-market trade on the news.
The company will remain headquartered in Seattle, while Alaska Airlines said it will expand its California presence.
The sale comes after the airline sold stock in a $353m initial public offering, pricing its shares at $23 each, in 2014. The California-based airline was launched in 2007.