Mr Wolstenholme has been with BAA for ten years and was most recently in charge of all capital projects across the operator’s seven airports.
He will start in his new role in February 2009.
Balfour Beatty chief executive Ian Tyler said: "Balfour Beatty Management plays an increasingly important role in the Group, providing much of the upfront thinking and management skills required to deliver complex projects for customers.
"I am delighted that Andrew is joining us, as we continue to develop our major projects capability and upstream professional services across the Group."
Mr Wolstenholme has left BAA with immediate effect before taking up his new post in February. BAA construction director Rob Stewart will takeover Wolstenholme's role on an interim basis until a new appointment is made.
He was previously a director at Arup and spent four years in the British Army.