Stephen Robson, 62, currently the 'number two' at the Archdiocese of St Andrews and Edinburgh, will take over from Vincent Logan, who stood down three years ago this month.
Bishop Robson had been the Auxiliary Bishop to shamed Cardinal Keith O'Brien before his fall from grace earlier this year, but his appointment is seen as a clear indication he was untainted by the scandal.
At the time Bishop Robson said he was "gobsmacked" by the revelations of sexual activity by the Cardinal stretching back decades.
His role during Cardinal O'Brien's time was to essentially carry out the administration that kept the east coast archdiocese functioning and he is seen in church circles as a good choice.
He will be appointed Bishop of Dunkeld, which covers the Dundee and Tayside area.
The appointment had been widely predicted in Catholic circles and leaves the Dioceses of Paisley and Motherwell vacant, with a replacement also required for the frail Bishop of Galloway, John Cunningham.
Bishop Robson said: "I am deeply honoured to have been chosen by Pope Francis as the next Bishop of Dunkeld. Dunkeld is a beautiful diocese set in the heart of Scotland and I look forward to living and working there, getting to know the clergy, religious and laity and accompanying them on their Christian journey."
The installation of the new bishop will take place in St. Andrew's Cathedral in Dundee very early in January on a date to be announced shortly.