The TV star, who played Finn Hudson in the hit show, passed away last month at the age of 31 due to a mixed toxicology of heroin and alcohol, reported E! online.
"I would like to thank all of Cory's supporters at this extremely emotional time," McGregor tweeted.
"Your support has been overwhelming, thank you!"
It was recently revealed that the Emmys will pay tribute to the actor.
Meanwhile, Monteith's exit from the show will deal directly with drug abuse.
'Glee's creator Ryan Murphy also said that he considered ending the show after he learned of Monteith's death.