Ashfield, according to a show spokesperson, will begin his run at the Eugene O'Neill Theatre August 23. He succeeds Grey Henson.
Ashfield has also been seen on the U.K. stage in Taboo, Fame, Jersey Boys and Legally Blonde. His screen credits include Call the Midwife and Sweeney Todd.
South Park creators-writers Trey Parker and Matt Stone and Tony-winning Avenue Q songwriter Robert Lopez collaborated on the script and score to The Book of Mormon, which earned nine Tony Awards, including those for Best Book, Best Score and Best Musical.
Co-directed by Parker and Casey Nicholaw, The Book of Mormon opened March 24, 2011, at the Eugene O'Neill Theatre. Both earned Tony Awards for their work.