The deal will help the oil and gas services giant expand its Norwegian offshore engineering business and gain access to markets involved with the heavy oil-producing Norwegian Continental Shelf.
Agility Projects, a subsidiary of Agility Group AS, will still be overseen by the company's chief operating officer Otto Søberg and run from its Sandefjord offices near Oslo, but will now operate within the Wood Group Mustang offshore division.
Headquartered in Texas, Wood Group Mustang employs almost 8,000 people worldwide and has completed more than 11,000 engineering projects.
The acquisition is expected to be completed, subject to meeting competition guidelines in Norway, in the third quarter of this year.
Steve Knowles, chief executive officer of Wood Group Mustang, said: "Agility Projects' reputation is very well-established in Norway and represents a strategically important acquisition for Wood Group Mustang as it increases our exposure to the greenfield and brownfield engineering markets on the NCS. Agility Projects complements Wood Group's existing engineering activities in Norway and recently we successfully collaborated in winning the Ivar Aasen topside engineering project in Norway."
Otto Søberg, chief executive officer of Agility Group, said: "The culture and core values of Agility Projects represent a perfect fit with Wood Group Mustang as we both focus on quality of service, customers and employees."
Oil and gas data firm Rystad Energy has forecast that $14 billion (£8.2bn) will be spent in the Norwegian offshore oil and gas engineering market between now and 2020.
Wood Group promised to pursue more acquisition opportunities after generating pre-tax profits of $412.8m (£247m), up 14 per cent, in 2013.
The listed group's biggest recent contract wins include a £300m package for BP in the North Sea awarded last December, and a £36m deal unveiled last month to work in the giant Shah Deniz site in the Caspian Sea.
At the end of June, when Wood Group updated the market on first-half trading , it said the engineering arm was performing in line with expectations.
Wood Group shares were up 6.5p at 766p.