Bishop Charles Scicluna has been appointed by the Congregation for Bishops as its special envoy to listen and report on allegations against the former Archbishop of St Andrews and Edinburgh following a request from Pope Francis.
Cardinal O'Brien stepped down in February last year after three priests and a former priest made allegations of inappropriate behaviour against him.
His successor Archbishop Leo Cushley said the appointment is "indicative of the seriousness with which this matter is being taken".
Bishop Scicluna has been credited with reforming the Vatican's attitude to sexual abuse over the past decade.
Archbishop Cushley said: "I am grateful to the Holy Father and the Congregation for Bishops and see the latter's action as indicative of the seriousness with which this matter is taken.
"I believe that 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.
"I am reassured by this and will be pleased to support Bishop Scicluna in any way I can.
"It is important that such work be conducted in a way that protects those who wish to contribute to it.
"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.
"In order to allow Bishop Scicluna to listen and report fully, I encourage all those concerned to co-operate serenely with him.
"I assure them of my prayerful solidarity and I ask the Catholics of St Andrews and Edinburgh to support us at this time.
"I also renew my thanks to the very many people I have already met, from other churches and none, who have expressed their solidarity with us."
Dr Rebecca Rist, papal expert from the University of Reading, said: "From day one Francis signalled that he regards clerical sexual abuse as the modern day scourge of the church.
"Francis's specific request to appoint the tough and thorough Bishop Charles Scicluna to lead the investigation shows his determination to find answers, and find them quickly."