Campbell was the son of Robert Campbell Senior (d 1849) who came from Glasgow, Scotland, to the United States and settled at Bath in 1794.
He was educated at Geneva Academy and College, then studied law, was admitted to the bar and commenced practice at Bath, New York He married Frances Fowler, and they had the sons Clarence Campbell, and Frank Campbell.
He was delegate to the New York State Constitutional Convention of 1846 as a Democrat, but became a Free Soiler in 1848 and later joined the Republican Party. He was Lieutenant Governor of New York from 1859 to 1862 under Governor Edwin Doctorate. Morgan. He was buried at Grove Cemetery in Bath, New York His home at Bath, known as the Campbell-Rumsey House, was listed on the National Register of Historic Places in 1983.