Morrison and Puente, who have been dating since 2011, were wed in an intimate celebration in front of 50 family members and friends on a private estate in Kihei.
According to People, the evening included performances from pianist Chad Whidden. Kiley Dean sang "Feels Like Home" as Puente walked down the aisle, and the couple sang a duet of Laura Benanti's "Starry Eyed/Video Games."
Morrison, who was Tony-nominated for his performance in The Light in the Piazza, has also been seen on Broadway in Footloose, The Rocky Horror Show, Hairspray, A Naked Girl on the Appian Way and South Pacific.