The board of consulting company Accenture PLC has named the head of the company’s operations in North America as its new chief executive.

Julie Sweet, 51 years old, will become CEO of Accenture and join the company’s board on Sept. 1. Since 2015, she has headed Accenture’s North American operations, a division that makes up nearly half of the company’s revenue. She started at Accenture in 2010 and has served as the firm’s general counsel and compliance chief.

Ms....