The musician recently signed up to play a Spanish teacher in the Fox show and has now begun filming scenes.
Martin tweeted a photo of himself with the cast on set, adding: "First day!"
Glee star Lea Michele also took to Twitter to express her excitement about Martin's guest role.
"I've known Ricky since I'm 8 years old [sic]!" she tweeted. "He was in Les Mis on Broadway with me in 1996! Crazy, huh?"
Michele also uploaded a photo with Martin on set, saying: "He's seriously the sweetest and such a great fit for our show!"
Helen Mirren, Pitbull and Gloria Estefan are among the other guest stars who have been linked to parts on Glee.
The show returns with a new episode on January 17 at 8/7c on Fox.
