"As I depart, I want to offer once again my sincere apologies to any person who has been abused by any priest of the diocese of Cloyne during my time as bishop or at any time," he said.
'Decades of abuse'
Magee, aged 73, had been a senior figure in the Vatican, previously serving as a private secretary to three successive Roman Catholic popes before being assigned to Cloyne.
He had apologised when the report into clerical child abuse by National Board for Safeguarding Children was first published at the end of 2008, but refused to resign.
Ken Murray, an Irish journalist, told Al Jazeera the image of the Catholic church in Ireland had "taken a bashing" over sex abuse allegations.
"This is yet another bad day for the image of the Catholic church in this country," he said.
Irish government-ordered investigations have documented decades of child abuse and cover-ups in the Catholic church.
Three reports published between 2005 and 2009 have documented how thousands of Irish children suffered rape, molestation and other abuse by priests in their parishes and by nuns and brothers in boarding schools and orphanages.
Irish bishops did not report a single case to police until 1996 after victims began to sue the church.
On Saturday, the pope apologised for decades of abuse, but took no action against bishops blamed for cover-ups.
Magee's resignation is the second from an Irish bishop to be accepted by Rome.
Donal Murray, former bishop of Limerick, had his resignation accepted within 10 days when he offered to quit last December.
He was criticised in an investigation into the Dublin Archdiocese over failures to report child abuse.