Fr. William Nolan is currently priest of Our Lady of Lourdes, East Kilbride, and Vicar General of the Diocese of Motherwell.
He's replacing Bishop John Cunningham who said he was 'delighted' at his successor.
Bishop-Elect Nolan said; "I am overawed to be appointed by Pope Francis as Bishop of Galloway.
"I already know some of the clergy and I look forward to working with them and with the people of the Diocese to help the faith flourish in the land where Ninian planted the seeds of faith so long ago.
"I wish to serve the Diocese as best I can, but knowing I am hindered by my failings and weaknesses, I ask everyone to pray for me."