Seán Barrett says it has been "a great honour and privilege"
The Ceann Comhairle says he will not be seeking re-appointment to the position in the next Dáil.
In a statement, Seán Barrett says: "It has been a great honour and privilege for me to serve as Ceann Comhairle for the 31st Dáil".
"However I will not seek or accept any nominations for the position of Ceann Comhairle during the next Parliamentary term".
"I look forward to participating in the 32nd Dáil and representing my constituents," he added.
Before his role as Ceann Comhairle, Mr Barrett served as Government Chief Whip and Minister for Sport in the Garrett Fitzgerald government.
He has also served as defence minister in the rainbow government led by John Bruton.
Up to now, the Ceann Comhairle has been selected by open vote when the Dáil meets after a general election.
However, new rules mean any incoming TD can put themselves forward for the post and be elected by secret ballot.