He was the son of Andromache (née Fotiadou) and Theocharis Ioannides Efstratiou (a steel worker), both immigrants from Greece.

[3] He studied acting with such prominent mentors as Howard Da Silva and played character roles on and off Broadway in his mid-twenties, supplementing his income as a night watchman and shooting-gallery barker.

In 1965, Constantine was cast as the historical John Chisum in the episode "Paid in Full", on the syndicated television anthology series Death Valley Days.

Constantine played a long-suffering anti-organized-crime agent in Walt Disney's caper film The North Avenue Irregulars (1979), where he appeared alongside Edward Herrmann and Cloris Leachman.

In 1993, Constantine appeared in the independent drama Question of Faith, starring Anne Archer and Sam Neill.

[6] On October 5, 1953, Constantine married actress Julianna McCarthy, whom he met while in the cast of Inherit the Wind.