Current Taylor Woodrow finance director also has experience heading up PFI projects.
Bickerstaff has been with the Taylor Woodrow group since 1982 and, in addition to his current role, has held a number of senior management and financial positions across the group.
Prior to becoming finance director, he was divisional operations director in charge of the group's PFI projects.
He is also a non-executive director of Construction Industry Publications Ltd, a subsidiary company of the Construction Confederation, specialising in books and publications for the Construction Industry.
David Jefferies, the chairman of Costain, said:"'I am delighted to welcome Tony Bickerstaff to Costain. He has considerable experience both in the industry and the finance arena. He will be an able successor to Charles McCole who has made a significant contribution to our successful recovery and whom we wish well for the future."