The 20-year-old, best known for his role as Weatherfield's Craig Harris, will take over from Duncan James in the part of Warner Huntington III from June 16.
Fleeshman's casting had first been rumoured last month but was not officially confirmed until today.
Speaking of his new role, the actor told the Daily Express: "It's nerve-wracking to start in a successful show - I'm paying my dues in reverse. But I'll give it everything. I can't wait."
Legally Blonde: The Musical also stars Sheridan Smith and Jill Halfpenny. The production opened at the Savoy Theatre earlier this year and is currently booking until February 20, 2011.