My Big Fat Greek Wedding became the highest-grossing romantic-comedy of all time with a $241.4 million domestic gross. It was based on writer-star Nia Vardalos' one-woman play and produced by Tom Hanks and Rita Wilson for just $5m.
"Michael was always the kindest person," Wilson wrote on Instagram. "He had time for everyone, and when you were with him he made you feel like you were the only person in the room. He will be with us forever in our hearts and for future generations who will watch his work."
Constantine initially auditioned for the part of Gus and told The Hollywood Reporter that he was anxious to read Vardalos' script, leery about how it might represent the Greek American experience.
"I was anxious about someone writing some Greek thing. Was it going to be baloney or was it going to be something by somebody who really knows Greeks? So I read the script and I said, 'Yes, this person obviously knows Greeks'," he said.
Vardalos paid tribute to Constantine on Twitter, writing: "Acting with him came with a rush of love and fun. I will treasure this man who brought Gus to life. He gave us so much laughter and deserves a rest now."
Constantine was the son of Greek immigrants. He started his career on stage and was on Broadway in the late 1950s and early 60s in such shows as Arturo Ui, The Miracle Worker and Inherit the Wind.
He made his big-screen debut alongside Mickey Rooney in The Last Mile and had roles in The Hustler, Don't Drink the Water, Prancer, The Reivers, My Life and The Juror.
Constantine was married and divorced twice. Survivors include his sisters, Patricia Gordon and Chris Dobbs.