Anderson, 52, succeeds Gerald Grinstein, 75, who will retire from the airline after leading it through bankruptcy proceedings.
The company emerged from bankruptcy court protection April 30.
Anderson, currently an executive vice president at UnitedHealth Group Inc., will take over Sept. 1, the same date Grinstein retires and steps down from Delta's board.
The board concluded Anderson possessed "the right blend of seasoned leadership, strategic skills, international experience and airline knowledge the company needs to navigate the industry’s challenges and capitalize on its opportunities," Chairman Daniel Carp said.
In addition to Anderson’s appointment, the board promoted Chief Financial Officer Edward Bastian to president and chief financial officer, reporting to Anderson, Delta said.
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