Mr Davies will takeover from current CEO Keith Cochrane on 02 April 2018.
The news comes following a profit warning by Carillion over the summer, when a review of the business unearthed a £845 million black hole in its finances.
Having been appointed Chief Executive of Wates in 2014, Mr Davies previously held a series of senior roles with BAE Systems plc over a 28 year period.
Carillion Chairman Philip Green said: "Andrew has the ideal combination of commerciality, operational expertise and relevant sector experience to build on the conclusions of the strategic review and to lead the on-going transformation of the business.
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"His experience and his people focussed personal style are an ideal combination for our business. We are pleased that he has agreed to join us and we are grateful to Keith Cochrane for his interim leadership of Carillion."
Mr Davies said: "It has been a privilege and a pleasure to work for the Wates Group, and I am proud of what we as a company have accomplished over these past four years. I have the greatest respect for the organisation, its heritage, and its people, who have continually impressed me with their commitment, integrity, professionalism and performance.
"In particular I would like to thank James Wates and the Wates Family for their guidance and support during my tenure as CEO. I look forward to working with the Board and the management team to ensure there is a smooth and orderly transition."
Wates' Chief Financial Officer, David Allen, will become acting Chief Executive on 10 November as the company hunts for a successor.
(LM/MH)
