Criss made the announcement on an appearance on "Live with Regis and Kelly" March 7. The CD is expected to be released in April.
No track listing for the CD has been announced. Criss and the group, which is voiced by real-life Tufts University a cappella group The Beelzebubs, debuted on the show with Katy Perry's "Teenage Dream," which hit No. 1 on Billboard's digital sales chart with the best sales in its initial week of any "Glee" single to date.
Covers of Train's "Hey, Soul Sister," Destiny's Child's "Bills, Bills, Bills," Robin Thicke's "When I Get You Alone" and Wings' "Silly Love Songs" followed, in various episodes of the Fox musical series. The March 8 episode of "Glee" will feature Criss and "Glee" regular Chris Colfer leading The Warblers in a performance of Neon Trees' "Animal." The group will sing Maroon 5's "Misery" on a future episode.
Best known for a "Harry Potter" musical parody that became a YouTube hit prior to his "Glee" appearances, Criss has also appeared on the series "Eastwick."
"Glee" airs Tuesdays at 8 PM ET on Fox.