Abney, 58, becomes the company's 11th CEO and will replace Scott Davis, 62, who will retire from the company. Davis will serve as non-executive chairman.
Abney's career at UPS, the Atlanta-based company, began in 1974 when he was a part-time package loader, the company said in a statement. As chief operations officer, he oversaw the company's logistics, sustainability and engineering programs.
"UPS has exceptional depth of management and has historically elevated senior internal leaders to the CEO role," said Duane Ackerman, a member of the company's board of directors. "After thorough consideration of candidates, the board believes David embodies the experience, vision and leadership skills necessary to lead UPS."
The appointment will become effective Sept. 1.