SAO PAULO, Feb 21 (Reuters) - Brazilian airline Azul's AZUL.N board of directors has approved a capital increase as part of an out-of-court restructuring that gave lessors equity in lieu of nearly $550 million in obligations, the company said late on Thursday.

The capital increase of up to 3.37 billion reais ($591 million) came through the issuance of new shares, Azul said in a securities filing, with fresh investment from controlling shareholder David Neeleman, a serial aviation entrepreneur who also founded U.S. airline JetBlue JBLU.O.

Neeleman currently holds 67% of Azul's voting shares, with the other 33% being held by shareholders of Trip, an airline Azul acquired in the early 2010s. He is expected to lose control of the firm as part of the restructuring, but remain a major shareholder.

In addition to the equity swap with lessors and an agreement with bondholders for fresh financing, Azul is eyeing a potential tie-up with rival Brazilian airline Gol GOLL4.SA.

($1 = 5.7022 reais)

(Reporting by Gabriel Araujo in San Paulo; Editing by Nia Williams)

((Gabriel.Araujo2@thomsonreuters.com; +55 11 5047-3352;))