Conway's son, Jim Conway Jr., who is a vice president at the Runnemede-based company, said his father died of cancer Sunday at his Ocean City home.
The elder Conway and his brother William, who both worked at the Sweden Freezer company in Philadelphia, began experimenting with the idea of delivering ice cream by truck in 1955 under the company name Dairy Van.
In 1956, Mister Softee was launched when the two brothers drove their first truck through Philadelphia, giving away green ice cream as a nod to their Irish heritage, said Jim Conway Jr.
The ice cream venture, which moved to New Jersey in 1959, eventually expanded to become a multimillion-dollar business with more than 600 trucks in 15 states.
James Conway Sr. served as vice president of privately held Mister Softee Inc. until he retired in 1998, and his brother, William Conway, who died in 2004, was president. The company is now run by the men's sons.
Jim Conway Jr. said his father's favorite Mister Softee flavor was vanilla, although he also loved Breyer's butter pecan.
"You never saw anyone eat ice cream like this man," said the younger Conway.
Mister Softee is famous for the distinctive jingle that plays over and over from the trucks as they cruise through neighborhoods.
In 2004, New York City noise officials wanted to silence the trucks' music, but the city backed down after a public outcry ensued. Now all ice cream vendors can play music, but only when the vehicles are moving.
James Conway Sr. was born in Philadelphia and earned a degree in business from the Wharton School at the University of Pennsylvania. He was a U.S. Navy veteran of the Korean War.
Besides his son, Conway is survived by his wife, Grace Roseman Conway, two daughters and nine grandchildren. A memorial service is scheduled for Friday in Haddonfield.