Gyllenhaal was announced to star in the leading role, but has since departed.
Potter's The Addams Family costar Heidi Blickenstaff will be on hand for a guest performance.
The annual Hollywood event will raise money for AIDS Project Los Angeles.
Nathan Lane and Megan Mullally star in the one-night-only gala performance.
Errico replaces Victoria Clark, who was previously scheduled to perform at the gala.
Diane Paulus, Lea DeLaria, Mark Fisher, and more will speak at the third annual Broadway event.
The 2014-15 Ahmanson season will also feature current Broadway hit musicals Cinderella and Matilda.
Lily Rabe, Hamish Linklater, and John Lithgow are set to star in the two newly announced Shakespearean favorites.
The event will also feature a book signing and discussion of the work.
The theater will also present world premieres of Carey Crim's Conviction and Adam Overett's My Life Is a Musical.