In an unprecedented move, Bishop Charles Scicluna, who has been investigating clerical abuse for a decade, will be dispatched to Scotland next week to take testimonies from those with information about the sexual misconduct allegations surrounding the Cardinal.
Complaints against other members of the clergy will also be taken on board.
Cardinal O'Brien's successor Archbishop Leo Cushley said the Maltese bishop would "listen to and report the testimony offered by past and present members of the clergy ... concerning any incidents of sexual misconduct committed against them by other members of the clergy whomsoever".
Cardinal O'Brien stepped down as Archbishop of St Andrews and Edinburgh in February 2013 after confessing to sexual behaviour spanning his time as a priest, bishop and cardinal.
In a letter to clergy in the Archdiocese of St Andrews and Edinburgh, Archbishop Cushley said Bishop Scicluna would visit betweenTuesday and Thursday, adding he had spoken to the Pope and to Cardinal Marc Ouellet, the prefect of the Congregation for Bishops, about the matter.
Bishop Scicluna is best known in religious circles for being given the task by then-Cardinal Joseph Ratzinger in 2005 to collect testimonies on serial sexual abuser, Mexican priest Father Marcial Maciel.
He served at the Vatican's Congregation for the Doctrine of the Faith until 2012, where he reviewed hundreds of case-files of priests who were eventually dismissed from the ministry for sexual abuse.
In his letter, Archbishop Cushley added: "I believe the Holy See is examining the 'lie of the land' and trying to establish more precisely the veracity of various assertions now before it.
"I would therefore ask you to put your faith in the process and encourage any of you who have something of significance to say about misconduct of individuals in the clergy to get in touch with Bishop Scicluna."
He said Cardinal Ouellet, the Canadian who was a favourite to succeed Pope Benedict, was "confident that the inquiry is the best method available of establishing the truth of the assertions and the way that will ultimately lead us to the end of this long and difficult road."
Archbishop Cushley said: "I believe this is a positive step towards truth and eventual reconciliation, this may not be an easy thing to do, but it is the right thing to do.
"It is also important that the Holy See take such steps as are necessary to establish and evaluate the serious allegations which have been made over the last 18 months or so.
"In order to allow Bishop Scicluna to listen and report fully, I encourage all those concerned to co-operate serenely with him."
According to reports, one of the priests who has made the allegations has claimed he was "quite happy that the Church has seen fit to act".