He replaces David Allvey who retires as the Annual General Meeting in May after seven years in the post.
Golby, a mechanical engineer, spent nine years at E.ON UK – then known as PowerGen – as chief executive during which time he oversaw the transformation of the company from the smallest UK player into one of the country’s leading integrated electricity and gas businesses.
He is also chairman of air traffic control company NATS and a non-executive director of National Grid and was formerly chairman of AEA Technology Group.
Golby was appointed a member of the Prime Minister’s Council for Science and Technology in June 2011 and has been chairman of the Engineering and Physical Sciences Research Council since April 2012.
He said: “I am honoured to have been asked to join Costain as chairman.
“It is a great British engineering success story with a strong heritage, outstanding brand and strong market positions. I look forward to playing a part in delivering further success as the Group accelerates its growth agenda.”