Doug Parker said Friday that enough shares were cast in favor of the merger to guarantee approval. The margin was not immediately available.
Owners of US Airways Group Inc. stock would get 28 percent of the shares in the combined company, with the rest going to creditors, employees and shareholders of American Airlines parent AMR Corp.
The deal is still being reviewed by antitrust regulators at the U.S. Department of Justice. It also needs the approval of the judge overseeing American's bankruptcy proceedings.
Critics of the merger worry that it will reduce competition and drive up prices. Similar complaints arose around the mergers of Delta and Northwest in 2008, United and Continental in 2010, and Southwest and AirTran in 2011. Antitrust regulators allowed all those deals to go through.
Those other mergers changed the industry landscape, creating giants that made it harder for US Airways and American to compete, Parker said.
The merger "creates a fourth strong competitor to United, Delta and Southwest," said Parker, who will become CEO of the combined carrier, which will keep the American Airlines name and be based in Texas.
If the American-US Airways deal goes through, those four airlines will control more than 80 percent of the domestic air-travel market.
The Justice Department could seek to have American and US Airways give up some takeoff and landing slots at Reagan National Airport outside Washington, D.C.
Parker predicted that regulators will allow the merger to go through, and said, and doesn't think the airlines should be forced to give up slots at Reagan.
American Airlines and AMR have been operating under bankruptcy protection since November 2011. The merger would take effect when AMR emerges from Chapter 11 as a new company, American Airlines Group Inc.
AMR creditors are voting through July 29 on the reorganization and merger and are widely expected to approve the deal. A federal bankruptcy judge in New York has scheduled an Aug. 15 hearing to consider approving the merger, which Parker predicted would take place by the end of September.
The airlines would operate separately for months, if not a couple of years, as they combine work forces, fleets, computer systems and frequent-flier programs.
About 50 members of the Service Employees International Union protested outside the building where the US Airways meeting was being held, and several spoke during the shareholder event. They demanded better pay and, in some cases, union representation for airport workers.