The move will see Rhead’s 550 staff integrated into Costain by the end of this year.
Rhead Group was established in 1985 and provides a range of solutions for the lifecycle of infrastructure, construction and asset management programmes primarily in the UK.
Blue-chip customers include National Grid, Wales & West Utilities and BAE Systems.
In the year ended 31 July 2014, Rhead Group generated revenues of £63.5m and earnings of £5.2m.
Rhead Group’s senior management team, including Nigel Curry, Rhead Group CEO, will remain with the business.
Rhead Group will join Costain’s Power sector and report into the Natural Resources division.
Costain is also combining all of its nuclear activities across the group into one unit which will report into the Infrastructure division to concentrate on the opportunities in the sector.
Costain chief executive Andrew Wyllie said: “We are delighted to announce the acquisition of Rhead Group which has a well-established reputation for its collaborative approach, focus on innovation and service delivery excellence.
“This transaction accelerates the development of Costain and further broadens our range of capabilities to meet the requirements of major blue chip customers, providing greater ability to deliver integrated solutions across the full lifecycle of a project.”