"Blackbird tells the story of Una and Ray. Fifteen years earlier, they had a relationship and haven't set eyes on each other since. Now she's found him again," press notes explained.
The show premiered at the Edinburgh International Festival in 2005 before moving on to London's West End where it won the Olivier Award for Best New Play in a production directed by Peter Stein.
The drama was subsequently produced off-Broadway in 2007 by Manhattan Theatre Club with Daniels playing Ray and Allison Pill, his future Newsroom co-star, playing Una. This earlier, New York production was also helmed by Mantello.
Williams, 35, was recently seen in the Broadway musical Cabaret.
Daniels, 60, last appeared on the New York stage in the premiere production of Gods of Carnage in 2009-10. His film credits include the upcoming The Martian and Steve Jobs.