Featuring heavily in Irish theatre for nearly twenty years, Fay was the first director of the Dublin Fringe Festival which he co-founded with Bedrock Productions.
He has also held the post of Literary Director of the Abbey Theatre, and in 2007 he was the Theatre Curator of the Kilkenny Arts Festival.
Fay said he was "delighted and deeply honoured" to take up his new post at the Lyric, describing it as "one of the most beautiful theatres on these islands".
He added: "It has a history of producing thought-provoking theatre and I want it to nurture and produce the best from our artists - writers, actors, designers and directors.
"The Lyric must maintain an ongoing dialogue with its audience to stimulate imaginations, to entertain and to pose difficult questions. I look forward to producing vibrant theatre with brilliant theatre-makers and artists at the Lyric."
Commenting on the appointment the Lyric Chairman, Mark Carruthers, said: "We are delighted to have secured Jimmy, who is one of the most highly regarded directors in the country, to lead the Lyric into the next phase of its development.
"His professional reputation, depth of experience and extensive theatre connections will ensure the Lyric is well-placed to stage top class, relevant theatre in the years to come. The whole team is looking forward to a bright future with Jimmy at the helm."
Fay will take up his new position at a date still to be announced.