May, who is currently the airline's senior vice president of finance and investor relations, will succeed Derek Kerr.
Kerr will remain at the carrier as vice chair, president of American Eagle and strategic adviser.
The move comes at a time when the carrier faces the task of fixing its debt-laden balance sheet amid a strong rebound in travel.
(Reporting by Nathan Gomes in Bengaluru; Editing by Sriraj Kalluvila)