Campbell was born in Waimate on 27 May 1925, the son of Mona Sevicke Campbell (née Jones) and David Brown Campbell. He was educated at Waimate High School, and then proceeded to study chemistry at the University of Otago, graduating Master of Science with second-class honours in 1948, and  PhD in 1953. His doctoral thesis was titled Some applications of acrylonitrile.
In 1950, Campbell married Ruth Florence Smith, and the couple went on to have three children.