Kirk, who has been in post for four years, will be replaced by the venue's current associate director Anthony Biggs.
Announcing his departure, he said: "Four years ago the Trustees asked me to take over the artistic helm at Jermyn Street Theatre, and to give it an identity as a producing theatre with a clear artistic output. I feel I have achieved that brief and it is now time for new leadership on the artistic level."
During his tenure, Kirk has presented a mixed programme of both rarely performed European and American classics and vibrant new plays and musicals. Highlights have included Charles Dyer's Mother Adam and Tennessee Williams' The Two-Character Play, as well as the current production, Trevor Nunn's revival of Samuel Beckett's All That Fall starring Michael Gambon and Eileen Atkins.
Kirk, who is leaving to pursue freelance work, including directing The Two-Character Play in New York next year, added: “All of us at Jermyn Street Theatre now look to this next phase with a core commitment to deliver a quality of work beyond its perceived station.”