Wills, who won the Panel Prize at this year's Foster's Edinburgh Comedy Award (formerly the Perrier) at this year's Edinburgh Fringe, said: "For over five years, I have had a West End season on my list of goals and I'm very happy that finally what seemed like a dream is becoming a reality. I am quietly screaming with excitement."
Billed as an "utterly unique comedy phenomenon", The Boy With Tape On His Face performs mimed sketches with a strip of gaffer tape over his mouth.
According to press material: "This is stand-up with no talking, drama with no acting and punch lines with no words."
The Boy With Tape On His Face, who arrives in the West End following an extensive UK tour, runs at the Duchess Theatre until 5 January 2013.