His resignation leaves Britain without a vote at an upcoming Rome church conclave to select a new pope, the BBC reported Monday.
O'Brien, 74, the archbishop of St. Andrews and Edinburgh in Scotland, apologized in a statement to anyone he had offended during his time as a priest.
"Looking back over my years of ministry: For any good I have been able to do, I thank God. For any failures, I apologize to all whom I have offended," he said.
"I do not wish media attention in Rome to be focused on me -- but rather on Pope Benedict XVI and on his successor."
Three priests and a former priest complained to a papal representative in early February about what they said was O'Brien's inappropriate behavior toward them in the 1980s.
O'Brien is known as a staunch defender of the Church's teachings on abortion, euthanasia and homosexuality. Last week he said he believed priests should be able to marry.
He had been planning to retire after the new pope was selected, ANSA reported.
Benedict accepted the cardinal's resignation, CNN reported.
A Vatican spokesman, the Rev. Federico Lombardi, said the pope had been informed of the allegations against O'Brien.