Twomey was named president in 2003 after serving for four years as chairman of Icann's Government and Advisory Committee.
He has told the board of directors that he will not seek another three-year term when his contract runs out at the end of 2009.
The announcement was made at the opening session of Icann's 34th International Public Meeting in Mexico City, which is being held to debate a variety of issues critical to the future direction of the Internet, including internationalised domain names, and new generic top-level domains.
"While I am deeply and personally committed to Icann and its success, I think this is the right time for me to move on to another leadership position in the private or international sectors," said Twomey.
"I am delighted to have taken part in building Icann's role in assuring a stable and secure Internet."
The industry was quick to praise Twomey's efforts. "I can think of no other person who has had more influence on the course of Icann's evolution than Paul. The board will be challenged to find a worthy and capable successor," said previous Icann chairman Vint Cerf.
Lynn St Amour, chief executive of the Internet Society, argued that Twomey's work in leading Icann had been central to ensuring the continued security and stability of the Domain Name System.
Twomey will stay on in the newly created role of senior president after the end of this year for a handover period with his successor, said Icann.
