"The company expects Mr. Lee, in his new capacity, to lead the brand's further global expansion by leveraging his overseas business operations expertise," Hyundai said in a statement.
"North America is an imperative market for the Genesis brand," it added.
The news follows the appointment this month of Mark Del Rosso, a former president of Audi America, to oversee Genesis operations in North America.
Genesis U.S. sales halved to 10,312 last year, although sales have picked up this year. The United States is the biggest overseas market for Genesis, which generated 72% of its sales in South Korea last year.
Before his stint at Hyundai Motor North America, Lee oversaw Hyundai's Brazil operations and the U.S. unit of advertising arm Innocean Worldwide.
Hyundai said in a recent earnings conference call that it has set up Genesis sales operations for China and Europe.
Hyundai Motor Group's heir apparent Euisun Chung introduced the Genesis brand in November 2015, bringing in Fitzgerald, a former Lamborghini executive, a few months later to help the automaker shed its value for money image.