In a statement, Ritter told PEOPLE that when he popped the question, "She cried. I was shaking and we were on a roof and no one fell off."
Satine, 25, who debuted on the Starz series a year ago, uploaded to Twitter on Thursday a photo of a sparking diamond engagement ring on her finger. Her message: "Future Mrs. Ritter!!!"
Ritter, 28, added, "I've found my bride at last," and later stated, "Thanks for all of your congratulations my friends, it means the world that you all are so kind-hearted. My face hurts from this glued smile!"
Reporting by JULIE JORDAN and KEVIN O'DONNELL