The group said the firm, established by chief executive Keith Wallace in 2009, will be combined with its ClerkMaxwell subsidiary to create a division called Costain Upstream.
EPC, which employs 75 people, provides services to oil and gas companies operating in the North Sea and generated a profit of £1.1m last year, on revenues of £11.7m.
Costain has paid £9.6m for the business, plus a further £1m for “excess cash”, but further payments may be due depending on its financial performance over the coming years. Wallace will remain with the firm to head up Aberdeen-based Costain Upstream.
Costain chief executive Andrew Wyllie said: “The formation of Costain Upstream will significantly enhance our position in this sector, and the acquisition of EPC Offshore will boost its growth, complementing the front-end engineering and operations capabilities we acquired with ClerkMaxwell two years ago.
“There is a sizeable addressable market for these highly complex services and we see further compelling opportunities to grow our oil and gas footprint both in the UK and internationally.”