King died Thursday in Dallas of the effects from a major stroke about a year ago, his son, Edward King, told The Associated Press.
Longtime Southwest CEO Herb Kelleher praised King for coming up with the idea of a discount airline that would serve Texas travellers. Kelleher said in a statement issued by Southwest on Friday that the notion of a low-cost, low-fare airline with quality service became a model not only in the U.S. but worldwide.
"The people of Southwest Airlines grieve with Rollin's family, mourn his absence, and thank him for his vision," Kelleher said.
The airline's current CEO, Gary Kelly, said King helped democratize air travel by making it more affordable.
Interstate air service was heavily regulated by the federal government in 1967, when King sat down with Kelleher, his lawyer, to map out the idea for a no-frills airline that would fly between Dallas, Houston and San Antonio. Edward King said his father got the idea for a Texas-only carrier by studying the success of Pacific Southwest Airlines, which operated within California.
The fledgling carrier had to survive several legal challenges by Braniff International and other airlines before its first flight in 1971. It began flying outside Texas in 1979, after deregulation, and is scheduled to begin international flights next week. Southwest is the nation's fourth-biggest airline company, with 2013 revenues of $17.7 billion.
King served on the board of directors from 1967, when the company was incorporated as Air Southwest, until 2006. He also flew as a Southwest pilot for a few years in the 1970s.
King was born in Cleveland, attended Case Western Reserve University and received a master's in business administration from Harvard, according to his son. He moved to Texas and was working in investment banking and acquired a small air-taxi service in South Texas before starting Southwest, according to the Texas State Historical Association.