Magee apologized to victims of any pedophile priests who were kept in parish posts since he took charge of the southwest Irish diocese of Cloyne in 1987.
"To those whom I have failed in any way, or through any omission of mine have made suffer, I beg forgiveness and pardon," the 73-year-old Magee said in a statement.
The pope on Saturday published an unprecedented letter to the Irish church criticizing some of its bishops for mishandling child-abuse cases. However, the letter accepted no Vatican responsibility for the decades that church officials spent covering up the abuse of children by its priests and nuns.
Benedict also has yet to accept resignation offers from three other Irish bishops who were linked to cover-ups of child-abuse cases in the Dublin Archdiocese, the subject of a major government-ordered investigation that published its findings four months ago.
Magee had been expected to resign ever since a Catholic Church-commissioned investigation into the mishandling of child-abuse reports in Cloyne ruled two years ago that Magee and his senior diocesan aides failed to tell police quickly about two 1990s cases.
The church and the Irish government suppressed the publication of that report's findings until December 2008, when Magee faced immediate calls to quit from victims' rights activists and some parishioners. He was accused of ignoring an Irish church policy enacted in 1996 requiring all abuse cases to be reported to police.
Magee remained Cloyne bishop in name but handed over day-to-day responsibilities to his superior, Archbishop Dermot Clifford, in March 2009.
"I wish him all God's blessings in his retirement," Clifford said of Magee. "I ask for the continued prayers and support of the lay faithful, priests and religious of the diocese of Cloyne for all those who have suffered abuse."
Separately, the state investigators who reported on the Dublin cover-ups have turned their sole attention to Cloyne and are expected to report their own conclusions later this year. Magee said he would answer their questions.
The church's Cloyne report found that Magee and his diocesan deputies fielded a range of complaints from parishioners about two priests from 1995 onward - but told the police nothing until 2003 and little thereafter. The report said Cloyne church authorities appeared to be solely concerned about helping the two priests, not protecting the children of the diocese.
One priest, who was accused of molesting a younger priest, was encouraged by Magee to resign. But the investigation found that the bishop shielded the abuser's identity from police - and considered such concealment "normal practice."
The other priest, a career guidance counselor in a convent school, was accused by several teenage girls and grown women of molesting or raping them since 1995. One complaint came from a woman who had a consensual sexual relationship with the priest for a year - then saw him develop an intimate relationship with her teenage son.
The church has declined to identify the two priests publicly by name. Neither has faced any criminal charges.
Magee, who was born in the Northern Ireland border town of Newry, served as a private secretary to three successive popes - Paul VI, John Paul I and John Paul II - from 1969 to 1982. He then served as the pope's master of ceremonies until 1987.
