Morrison will play The Grinch in the London theatre production, which will be filmed for TV and air in the U.S. on 9 December (20).
Newcomer Amelia Minto will play Cindy-Lou Who, while the rest of the ensemble will be made up of musical theatre actors from the West End.
Morrison said in a statement, "In what has been an extremely challenging year for us all, it is an honour to bring some holiday cheer into viewers' homes this December."
"My wish is to bring some Who-ville magic to this holiday season and, while the pandemic presents some challenges in bringing a stage production to life, we are excited to present a unique version of this seasonal favourite in a new creative and imaginative way."
The performance will take place at the Troubadour Theatre in London, and features a book and lyrics by Tim Mason and music by Mel Marvin. The staging is directed by Max Webster and Julia Knowles will direct for TV.
The musical will be broadcast on America's NBC network, and is the latest to be produced for a TV event following previous productions of "The Sound of Music", "Peter Pan", "The Wiz", "Hairspray", and "Jesus Christ Superstar Live in Concert".