The announcement came a day after a report by the British Sunday newspaper The Observer that three priests and one former priest leveled allegations against O'Brien that date back 30 years.
Speaking in London on Tuesday, one of Britain's most senior Roman Catholics, the former Archbishop of Westminster, Cardinal Cormac Murphy-O'Connor, described the circumstances of O'Brien's resignation as "very sad."
Murphy-O'Connor said that it was O'Brien's decision to step down and that he had not been forced or asked to do so. He described O'Brien as a "very honest man."
An apostolic administrator, most likely a senior bishop, will examine the allegations against O'Brien, Murphy-O'Connor said.
He also said he was in no doubt that there needs to be reform within the Roman Catholic Church and that the issues being raised now need to be addressed "at the highest level."