Harrison is best known for his role as Neil Sutherland in E4 comedy series The Inbetweeners. Other TV appearances include A Very English Scandal while stage credits include Step 9 and The End Of The Pier.
He will takeover from Jack McBrayer in the role of Ogie. McBrayer plays his final performance on June 15 with Harrison making his debut on June 17.
In a post on Instagram, the actor joked with fans: "As you some of you may already be aware, I will be taking over the role of Ogie in the musical Waitress at the Adelphi Theatre from the 17th of June. What you're probably not aware of is that I've stipulated in my contract that I only be paid in pies. It's going to be great."
Harrison joins the recently announced Lucie Jones and Ashley Roberts, who will be taking over as Jenna and Dawn respectively. They will also begin performances on June 17.
Other cast include Marisha Wallace as Becky with Peter Hannah as Earl, David Hunter as Dr. Pomatter and Shaun Prendergast as diner owner Old Joe.
Completing the current cast are Kelly Agbowu, Piers Bate, Nicole Raquel Dennis, Michael Hamway, Peter Hannah, Stephen Leask, Chris McGuigan, Olivia Moore, Nathaniel Morrison, Sarah O’Connor, Leanne Pinder and Charlotte Riby.
With a score by Sara Bareilles, a book by Jessie Nelson and direction by Paulus, Waitress features a ground-breaking, all-female lead creative team.
It tells the story of Jenna a waitress and expert pie-maker who dreams of a way out of her small town and rocky marriage.