The change is an abrupt shift for a company that had stable management for 20 years. Mr. Jackson had run AutoNation from 1999 until early this year, and he turned the company into a consistent profit-maker. On Monday, AutoNation reported a 3 percent rise in second-quarter net income, to $101 million. The increase came despite a slowing of new-vehicle sales in the United States. Revenue declined slightly, to $5.3 billion.

“Our strategy remains unchanged,” Mr. Jackson said.

AutoNation shares closed at $41.95. The stock is up about 18 percent since the beginning of the year.

Under Mr. Jackson’s leadership, AutoNation had become an influential player in the auto industry. A decade ago, Mr. Jackson publicly criticized the Detroit automakers for producing more vehicles than consumers were willing to buy and offering profit-eating incentives. Those practices contributed to the collapse that sent General Motors and Chrysler into bankruptcy.

Ms. Miller, 47, is a graduate of James Madison University in Harrisonburg, Va., and has spent 18 years in the auto retail sector. She joined AutoNation in 2009 and was named chief financial officer in 2014.