Johnston, 55, will join the company's board on July 1. Sullivan will continue to serve as chairman until his retirement at the end of the year.
Johnston joined Clorox in 1981 and has served as president and chief operating officer since 1999, responsible for U.S. and international operating divisions, and the company's sales, marketing, product supply, and research and development functions.
"In accordance with corporate governance best practices, in addition to considering Jerry, the board conducted a comprehensive external search," Sullivan said in a statement. "That process confirmed the board's belief that Jerry is the right person to lead the company forward."Clorox shares on the New York Stock Exchange rose 1.9%, or 81 cents, to $43.10 in Thursday afternoon trading.