Cowboys spokesman Rich Dalrymple confirmed that Avezzano died in Italy. He had moved to Milan earlier this year to coach an Italian Football League team, the Milan Seamen. That team said on its website that Avezzano died of a heart attack. Attempts to resuscitate Avezzano were unsuccessful, the team said.
Known affectionately in the Dallas area as "Coach Joe," he maintained a high profile after he left the Cowboys when Bill Parcells was hired as head coach in 2003.
"Joe Avezzano was a very special part of our Dallas Cowboys family and our organization's history," Jones said in a statement released by the team. "No one enjoyed life more than Joe, and no one that I know had a greater appreciation for the people that he loved and the lives that he touched. There was no one else like him."
"Joe Avezzano was a great coach and a super guy," NFL spokesman Greg Aiello said. "We are saddened by his loss."
In February, Avezzano took over the Seamen. Italians in Dallas threw Avezzano a send-off party before he left, Dallas television station WFAA reported.
"I am the long lost heir to the throne," Avezzano joked, according to the station. "They've been looking for me in Italy for years. Now they've found me and I'm going back and I will return to Avezzano. And that's going to be part of my travels."
Associated Press Writer Frances D'Emilio in Rome contributed to this report.