Peltz was born in 1942 in Brooklyn, New York. He attended the Wharton School of the University of Pennsylvania from 1960 but left in 1963 without a degree, and went to work driving a delivery truck for A. Peltz & Sons, the food distributor his grandfather founded in 1896. With his brother Robert he grew it over 15 years into an institutional frozen-food business, and in 1973, with partner Peter May, took the company, then called Flagstaff Corp., public.
In 1983 Peltz and May bought a stake in Triangle Industries and built it into the world's largest packaging company before selling it to Pechiney in 1988. In 1997, through Triarc Companies, they bought Snapple from Quaker Oats, and sold it with other beverage brands to Cadbury Schweppes in 2000.
In 2005 Peltz, May and Ed Garden founded Trian, which has invested in companies including Heinz, Cadbury, Kraft Foods, Wendy's, DuPont, Mondelēz, PepsiCo, State Street and Procter & Gamble. He became a non-executive director of Unilever in May 2022 and sought a seat on Disney's board in 2024 without success. Trian and General Catalyst completed the take-private of Janus Henderson on June 30, 2026, and a July 2026 Form D lists Peltz, his son Darren Peltz and May among Jupiter Topco's directors.