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Liebert is currently the chief operating officer at financial services company USAA and will take over his new job on March 11.
He has served as executive vice president-stores at home improvement chain Home Depot where he was responsible for international sales, strategy, execution and operations.
Jackson said last September that he will step down as CEO at the largest U.S. auto retail chain and will stay on as executive chairman of the board until 2021.
The company's shares have more than tripled since Jackson became CEO in 1999 after the company's founder Wayne Huizenga hired him from Mercedes-Benz USA, where Jackson was president.
AutoNation also reported a 4.8 percent drop in fourth-quarter revenue on Friday, as the largest U.S. auto retail chain sold fewer new vehicles.
AutoNation's net income from continuing operations fell to $92.9 million, or $1.02 per share. Revenue fell to $5.41 billion from $5.68 billion.