This will be Henry's second performance at the South Bank venue; his first was in a production of Shakespeare's The Comedy of Errors in 2011.
Henry confirmed his involvement in the play to BBC London Radio's Robert Elms, explaining that he has been working with director Michael Buffong.
Referring to his recent reinvention as an award-winning stage actor, he added: "I get to improvise and mess about so the comedy impulse isn't dying on the twig, it's still there."
He previously Tweeted that he's been working with Buffong on a one-man show:
Been working on a One Man Show with Michael Buffong at the national theatre studios all week. Thanks Mike - you are a don!— Lenny Henry (@ITISLENNYHENRY) July 6, 2014
Henry has taken on the role of Pryor before; he impersonated him in his 1989 standup show Live and Unleashed, portraying him as one of his comedy heroes.
Richard Pryor died in 2005 having battled drugs, multiple sclerosis and other troubles throughout his life. He was best known for his controversial routines that dealt with racism and other social issues in America. He also found a great deal of success in the film industry, co-writing movies including Stir Crazy and Blazing Saddles.