The Birmingham office is part of Costain chief executive Stuart Doughty's plan to increase the group's turnover 15% from its current £386m.
Thompson's appointment is the latest in a series as Doughty assembles a new senior management team to lift the company's performance.
He is also recruiting a finance director and a managing director to head the company's building division. Doughty plans to hire up to 400 staff to handle the expected growth.
Costain has recently appointed Mark Lye, formerly of Kier, procurement director and David Swann, who joined from contractor Dean & Dyball, business development director.
Swann, who started his £120,000-a-year job last week, will be responsible for major building projects, regional work and the construction part of PFI deals.
Costain has three equity stakes of up to £3m in PFI projects. Doughty wants to increase this.