The couple tied the knot in an intimate ceremony with close friends and family in New York on Wednesday, July 4, reports People.
Debolt proposed to Ramirez during their Paris trip last year.
Ramirez, a Tony-winning Broadway actress, plays Callie Torres in the ABC medical drama Grey's Anatomy.
On the show, Torres was divorced from George O'Malley (T.R. Knight) and married her partner Arizona Robbins (Jessica Capshaw).
Ramirez said she is proud of her same-sex marriage storyline.
"I've gotten tons of positive feedback," she said. "We offered up romance that a gay couple could relate to, and that's very inclusive. I felt honoured to tell that story."
Watch a clip of Grey's Anatomy below: