Fred DeLuca, who in 1965, at 17, borrowed $1,000 to open a sandwich shop in Bridgeport, Conn., to help pay college expenses and parlayed that experience into building Subway, the world’s largest chain of fast-food franchises, died on Monday. He was 67.

Subway confirmed his death in a statement but did not provide the cause or location.

In 2013, while traveling around to visit with franchisees, Mr. DeLuca became ill and was ultimately found to have leukemia. Since then, he had been receiving treatments and still overseeing the brand as chief executive, but he recently named his sister, Suzanne Greco, president to run Subway’s day-to-day operations, the company said.

A gregarious, hands-on chief executive, Mr. DeLuca ran those operations for decades, personally signing company checks, making corporate decisions, traveling the country in an old car and stopping at Subway outlets incognito to sample the food and service and talk with franchise owners and customers.

His first sandwich shop, named Pete’s Submarines to acknowledge the loan from his friend Peter Buck, was not a success. Its name had to be changed after his local radio advertisements, delivered in his native Brooklyn accent, confused many listeners, who thought he was saying “Pizza Marines.”