Entitled "Still Got Tonight," Allen penned the song with Andrew Frampton and Steve Kipner. Morrison's self-titled recording is due May 10.
The recording also features a duet with Oscar winner Gwyneth Paltrow on "Over the Rainbow."
Morrison will begin a 20-city U.S. concert tour this summer, launching June 18 at the Orpheum Theatre in Minneapolis.
Morrison received a Tony nomination for his work in Light in the Piazza and also appeared on Broadway in South Pacific, Hairspray, A Naked Girl on the Appian Way, The Rocky Horror Show and Footloose. On "Glee," he plays high school show-choir director and Spanish teacher Will Schuester.