They join the previously announced Jonathan Groff, Hannah Waddingham and Clive Rowe.
Peters, who will play J.B. Biggley, is a veteran of London musicals, including Guys and Dolls (National Theatre), Five Guys Named Moe (which he co-created) and Porgy and Bess. He is best known internationally for his TV appearances in "The Wire" and "Treme."
Erivo, who will play Rosemary, is currently appearing in A Midsummer Night's Dream at Liverpool's Everyman Theatre, and later this year will reprise her performance in the Menier Chocolate Factory production of The Color Purple on Broadway.
The musical will be directed by Jonathan Butterell, with Mike Dixon as Musical director conducting the Royal Philharmonic Orchestra.
To book tickets, visit http://www.southbankcentre.co.uk/whatson/how-to-succeed-in-business-wit-90403?dt=2015-05-19.
