Sunstone, which manufactures pipelines for clients in the Canadian oil and gas industry, employs 70 staff and achieved sales of C$21m last year.
Aberdeen-based Wood, which will rebrand Sunstone as Wood Group Mustang, said the deal complements its existing presence in Canada, where it employs about 1300.
Sunstone, which was established in 1994, specialises in developing pipelines and facilities to transport and process natural gas, natural gas liquids, conventional crude, heavy oil bitumen, and other petroleum products. It will continue to be run by the existing management team, led by president Barry Bauhuis.
A spokeswoman said it positions Wood Group Mustang for further growth in Canada, noting the country holds the world's third largest oil reserves. It is also the world's third biggest producer of natural gas.
More than half of the country's oil is produced in the oil sands region in western Canada and is transferred via pipelines for processing in eastern Canada. Pipelines are also needed to transport oil and gas to US refineries.
Wood Group has identified C$62bn of Canadian pipeline projects in development or under construction.
Steve Knowles, president of Wood Group Mustang, said: "The Canadian pipeline system is expected to expand to ensure access to markets for oil and gas produced in western Canada. The acquisition will strengthen our ability to provide clients with services in this area."
Shares in Wood Group closed down 5.5p at 761.5p.