Campbell’s father, a distinguished soldier, was a kinsman of the Duke of Argyll and the Earl of Breadalbane, for both of whom he had acted as manager of their estates.
During the seven years’ war Robert Campbell served as major, and subsequently lieutenant-colonel of the Fencible Men of Argyll, a regiment raised by the Duke of Argyll. On its disbandment in 1763 he retired, purchased the estate of Inverawe from his niece Janet Campbell, and lived near Edinburgh on his estate of Drummore. Alexander Carlyle records:
Our neighbourhood was enriched by the residence of a very valuable man, Lieutenant-Colonel Robert Campbell of Finab, a man of first-rate understanding and ability. He had been in the Duke of Cumberland’s war, and was captain of grenadiers in the 42nd regiment, but had been much disgusted with the Duke of Cumberland, and not having good health, he left the army ... He was very sociable and liked golf ... The Colonel had read very little but he had taken a more comprehensive view of men and affairs than almost any person I ever knew.
In the autumn of 1766 Campbell was selected by his former commander, the Marquess of Lorne, to replace Lord William Campbell as member for Argyll.
On the death in September 1771 of Sir Robert Murray, receiver general of customs, Mrs. Anderson, landlady of the British Coffee House, reported in her newsletter to her Scottish customers:
Campbell spent the rest of his life in Scotland, a very rich man, exercising considerable influence in the Argyll interest in Perthshire and Argyll.