"Jane steps into this critical role bringing with her decades of experience as both a leader and pioneer in our industry," United Chief Executive Oscar Munoz said in a statement.
Garvey's appointment to the non-executive role comes a month after the previous board chairman, Robert Milton, and a director, Laurence Simmons, announced their resignations.
United's executive suite has been plagued by internal turmoil, with Chief Financial Officer Andrew Levy last week stepping down from the role.
Garvey brings regulatory experience to her new role. She was the first woman to lead the FAA and headed the agency during the Sept. 11, 2001 attacks.
Garvey has served on United's board since 2009 and is the North America chairman of Paris-based Meridiam development and investment firm.
These corporate shuffles come as United seeks to ward off additional federal oversight in the wake of various customer service failures.
The carrier is also struggling to impress investors and improve its lagging financial performance as compared to larger rivals American Airlines and Delta Air Lines.
Shares of United closed up 1.34 percent.
(Reporting by Alana Wise; editing by Cynthia Osterman, Tom Brown and Diane Craft)
By Alana Wise