Wolstenholme, who has been with BAA for 10 years and latterly responsible for all capital projects across the operator's seven airports, will join Balfour Beatty's consultancy business 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."
Wolsteholme joins Balfour Beatty Management at a crucial time as the firm mounts a joint bid with Parsons Brinckerhoff to become both Crossrail's programme manager, managing the overall scheme, and its project delivery partner, managing the central London tunnelled section of the job.
As BAA capital projects director Wolstenholme was responsible for Terminal 5 at Heathrow and was deputy construction director on the Heathrow Express. He was previously a director at Arup and spent four years in the British Army.
He 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 successor is found.