Belfast-born Ellis was best known for playing Bert Lynch in BBC police drama Z-Cars, which ran from 1962 to 1978.
He studied at Belfast's Methodist College, Queen's University and at the Bristol Old Vic before starting his acting career at Belfast's Group Theatre in 1952.
His career also saw him star in television series including Doctor Who, In Sickness And In Health, Ballykissangel and Only Fools And Horses.
He played bullying father Norman Martin in the 1982 production of Too Soon To Talk To Billy - the first of a trio of Graham Reid plays focusing on working-class Ulster Protestants.
Hollywood star Sir Kenneth Branagh, who appeared as his son, paid tribute, saying: "James Ellis was a great inspiration to me, and many other actors from the North of Ireland.
"I was blessed to begin my career working with him, and I will never forget his generosity to me. He was a highly intelligent, funny, and kind man, and a tremendous actor."
Peter Johnston, director of BBC Northern Ireland, said: "We are saddened to hear about the death of Jimmy Ellis. He was a major talent from Northern Ireland, famous for his roles in Z-Cars and the Billy plays.
"He will be deeply missed by all his colleagues on screen and on stage."