The Catholic Primate of All-Ireland joined religious and political figures in praising the Pontiff's eight-year tenure.
"I think it is a profound act of humility, a conscientious and responsible decision to hand over the ministry of the successor of Peter at a time of great challenge in the church and for faith in the modern world," he said.
Pope Benedict, 85, will leave on February 28. He is the first Pontiff to resign in nearly 600 years and the decision sets the stage for a conclave to elect a new Pope before the end of March.
Archbishop of Dublin Diarmuid Martin said the Pope's decision to resign was courageous. "Who knows how long he has to live? Only himself and his advisers know that," Archbishop Martin said. "But to do this, shows he has that interior freedom within himself."
He also praised the freedom Pope Benedict showed in speaking out against the "filth" in the Catholic Church regarding sex abuse scandals.
"On behalf of the Government and people of Ireland, I would like to extend best wishes to His Holiness Pope Benedict XVI following his declaration today that he intends to step down from his office," Mr Kenny said. "This is clearly a decision which the Holy Father has taken following careful consideration and deep prayer and reflection.
Mr Higgins said he had written to the Pope expressing his good wishes on his decision to retire.
"In his letter, President Higgins acknowledged the scholarship and personal commitment that Pope Benedict brought to his leadership of the Roman Catholic community over the past eight years and wished him every peace and fulfilment in his retirement," the president's office said in a statement.