He will be succeeded as non-executive chairman by chief executive of BAE Systems Mike Turner CBE on 1 November.
Mr Turner will re-join the board of Babcock as a non-executive director on 1 June. He previously served between 1996 and December 2005.
Mr Campbell joined the board when he was appointed group chief executive in October 2000 and went on to be executive chairman from 2001 to 2003.
He said: “It is with some regret that I stand down after an exciting and, I believe, successful eight years, in which we have transformed Babcock from an unfocused engineering company into a dynamic support services provider.
“A successful company can be judged not only by its financial performance and return to shareholders, but also by its ability to provide orderly and timely succession.”