Mr. Smith, 57, said in a statement that he was leaving because he wants to stay close to family in Georgia. Wendy’s announced last month that it would move its corporate headquarters from Atlanta back to Dublin, Ohio, as another step in its breakup with Arby’s.

Mr. Brolick, 63, starts on Sept. 12 and will relocate to the Dublin area from Irvine, Calif.

Mr. Brolick is the chief operating officer of Louisville, Ky.-based Yum Brands but worked for Wendy’s for 12 years before leaving for Yum in 2000. He is also the president of Yum’s AW All American Food Restaurants and Long John Silver’s. However, Yum has been trying to sell those chains since January, saying they don’t fit its long-term growth strategy.

Yum Brands also owns Taco Bell, Kentucky Fried Chicken and Pizza Hut. It has increased both net income and revenue in every quarter for the past year.

Mr. Smith was C.E.O. of Arby’s, which was owned by Nelson Peltz, the hedge fund magnate who is Wendy’s chairman, when Mr. Peltz decided to buy Wendy’s as well in 2008. Mr. Smith became the chief executive of the combined company. The marriage of the two companies was short-lived. By the end, Wendy’s was the driver instead of the passenger, and this summer it sold Arby’s to a private-equity firm in Atlanta.

In August, Wendy’s reported second-quarter results that excluded Arby’s. Revenue rose 2.5 percent, after falling for four of the five previous quarters.

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