In his statement, Cardinal O'Brien, who turns 75 - the normal retirement age for bishops - on March 17, also explained his decision to skip the Pope's election.
"I do not wish media attention in Rome to be focused on me - but rather on Pope Benedict XVI and on his successor," he said.
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This is the first time a cardinal will stay away from a conclave because of a scandal-hit reputation, according to Ambrogio Piazzoni, the vice prefect of the Vatican library.
While accepting O'Brien's resignation, Benedict XVI also issued a "Motu Poprio," a legal document which slightly changes the 1996 Vatican law ruling the Pope's election.
One rule established that conclaves cannot begin until at least 15 days after a papacy's end. This was due to the fact that popes almost always die in office.
Since Benedict announced on February 11 that he would retire on February 28, cardinals from around the world would have enough time to prepare for the conclave.
"The cardinals will be permitted to bring forward the start of the conclave, if they are all present," the papal decree said.