Denise Morrison will succeed the 59-year-old when he leaves the company. The board elected her as chief operating office effective on Friday. Morrison has served as president of the company's North America Soup, Sauces and Beverages unit since October 2007.
Conant had been CEO and president since January 2001.
"The legacy of his wide-ranging contributions and sterling personal values will long endure at Campbell," Chairman Paul Charron said of Conant in a news release.
Morrison, 56, will lead soup, sauces and beverages in the U.S., the international division and Pepperidge Farm in her new role. All other functions will continue to report to Conant, the company said.