Philip Tartaglia will govern the Roman Catholic Archdiocese of St Andrews and Edinburgh until a permanent successor is appointed.
The pope named him as apolistic administrator after Cardinal O'Brien stepped down from the post on Monday amid allegations of "inappropriate" behaviour towards fellow priests.
Cardinal O'Brien has denied the allegations and is taking legal advice.
Archbishop Tartaglia said: "These are painful and distressing times for the archdiocese.
"I also feel pained and distressed.
"With the grace of God, I will do my very best to oversee and govern the archdiocese until the appointment of a new archbishop. I ask for your prayers."
With Cardinal O'Brien's resignation from the post, the Archdiocese is known as a "vacant see" and remains so until the appointment of a new archbishop.
The apostolic administrator governs with the authority, obligations and rights of a diocesan bishop until then.
Cardinal O'Brien is now Archbishop Emeritus of St Andrews and Edinburgh and has no role in the governance of the diocese.
A statement from the Scottish Catholic Media Office said: "The Holy Father, Pope Benedict XVI, has appointed the Most Rev Philip Tartaglia, Archbishop of Glasgow, as apostolic administrator of the Archdiocese of St Andrews and Edinburgh.
"With immediate effect, Archbishop Tartaglia will govern the Archdiocese of St Andrews and Edinburgh until a new Archbishop is appointed."
Cardinal O'Brien, who was Britain's most senior Catholic cleric, said he will not travel to Rome for the conclave to elect the next pope to avoid becoming a focus of media attention.