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.

Southwest Airlines (LUV) reached a settlement with activist investor Elliott Investment Management, ceding six board seats to the firm seeking control over the struggling airline.