The series, presented by Thirteen/WNET New York, is scheduled to premiere on Oct. 19, 20 and 21 on PBS.
"I am delighted to play a role in such an ambitious and important television project, and to `return' to Broadway once again," said Andrews. "There's nothing quite like a Broadway show to make our spirits soar and give us insight into America's very culture and history."
The Oscar-winning star of "Mary Poppins" began her American career on Broadway at 19 in "The Boyfriend." She followed that with Tony-nominated performances in "My Fair Lady" and "Camelot."
She was nominated for the Tony again when she returned to Broadway in 1995 for the stage version of her hit movie "Victor/Victoria."
"Broadway: The American Musical" was created by filmmaker Michael Kantor, whose credits include work on producer Ken Burns' "The West" and Ric Burns' New York series. Kantor wrote, produced and directed "Quincy Jones: In the Pocket."