Mr Wolstenholme will take up the position following a meeting with the Construction Minister Nick Boles on 21 October.
He will replace Sir David Higgins.
The council, which meets four times a year, was created in 2013 to work between industry and government to identify and deliver actions to improve efficiency, skills and growth in UK construction.
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Speaking on his appointment, Mr Wolstenholme said: "I am delighted to be taking over as the co-chair of the Construction Leadership Council at a time when building new infrastructure is at the heart of the government's plans to foster sustainable economic growth across the UK."
Construction Minister Nick Boles said: "The new Construction Leadership Council will bring together key industry leaders to deliver effective change. As chairman Andrew brings the unrivalled experience of managing Europe's largest infrastructure project and construction roles across the world.
"He will take over from Sir David, who has provided invaluable leadership for the construction industry at a key time of recovery and growth."
(LM/CD)
