Dundee was 90 and died of a heart attack on Wednesday in Clearwater, Florida, according to the Miami Herald.
The trainer suffered a blood clot on his return trip from celebrating Ali's 70th birthday in Louisville, Kentucky, and was admitted to a Clearwater-area hospital, the Herald reported.
He died after being transferred to a rehabilitation center.
"He was recuperating and coming along quite well," the trainer's son, Jim Dundee, said according to the paper. "He was already making plans to take a trip to Las Vegas for another event in two weeks."
Dundee was hired to train Ali in 1960 and remained with the boxer until his fight with Larry Holmes in 1980.
Known as a quick thinker and strong motivator, Dundee was also asked to help Leonard in 1976 and was in George Forman's corner when he knocked out Michael Moorer to win the heavyweight crown at the age of 45 in 1994.
"Thankfully, the whole family was with him," the younger Dundee said of his father's death. "We have lost a great man."
Angelo Dundee was inducted into the Boxing Hall of Fame as a non-participant in 1992.