Day, who was seen on Broadway in 2011 in Richard Eyre's production of Private Lives opposite Kim Cattrall, joins the previously announced principals Richard Fleeshman, Jenna Russell, Jonathan Slinger and Marc Elliott.
The company also includes Chris Bennett, Katie Bernstein, Alasdair Buchan, Cory English, Madeleine Harland, Rosanna Hyland, Karis Jack, Julie Jupp, Aaron Lee Lambert, Mark Meadows, Joel Montague, Jo Napthine, Jeff Nicholson, Adam Pearce, Charlotte Scott and Matthew Seadon-Young.
Day was last seen on the London stage in The Low Road at the Royal Court. Other recent credits include The Taming of the Shrew at Shakespeare's Globe and Twelfth Night at the National. His TV credits include "Sherlock" and "Musketeers."
Jamie Lloyd will direct the musical, which has music and lyrics by Mark Hollmann and book and lyrics by Greg Kotis. It is produced by Julian Stoneman Associates and The Araca Group. It is designed by Soutra Gilmour, with choreography by Ann Yee, lighting design by Adam Silverman, sound design by Terry Jardine and Nick Lidster, orchestrations by Bruce Coughlin and musical supervision by Alan Williams.