Southwest Airlines and Elliott Management are near a settlement which will stave off a proxy fight at the carrier, a person familiar with the matter said. The deal will give Elliott a sizable representation on the company's board but would fall short of a majority.

Southwest Airlines has given in to demands from Elliott Investment Management after months of an ongoing battle and agreed to restructure board leadership in a new settlement.

"I believe Southwest’s best days lie ahead," said Gary Kelly, who will soon step down as board chair as part of the deal.