Finneran won her Tonys for her work in "Promises, Promises" and "Noises Off."
"Miss Hannigan is one of the great musical comedy roles and I cannot wait to play her, in all of her deliciously evil glory. I played Hannigan in my parents' living room when I was 8 years old and the chance to play her in this new Broadway production is a dream come true," Finneran said in a statement issued to Playbill.com.
The show is to begin previews Oct. 3 and will open Nov. 8 at the Palace Theatre.
"Annie" features music by Charles Strouse, lyrics by Martin Charnin and book by Thomas Meehan. It is based on the newspaper character "Little Orphan Annie" by Harold Gray. The new stage production is directed by three-time Tony Award-winner James Lapine and choreographed by Tony Award-winner Andy Blankenbuehler.
Producers said 11-year-old Lilla Crawford will play the title role.