Moir was the son of the minister of Peterhead, Aberdeenshire, and the nephew of James Byres, the famous Scottish antiquarian in Rome. Moir was in Edinburgh in 1803, when he was described as a landscape painter. After studying in Italy, he based himself in Edinburgh but he spent part of every year back in the north east. Working mainly as a portrait painter, he seems to have regularly been in financial difficulties. In the 1840s he returned permanently to Peterhead. His sitters include many significant figures from Aberdeenshire area.