Davies will replace Keith Cochrane who will continue to lead Carillion as interim chief executive officer until then.
He faces the most challenging job in construction with Carillion’s debt expected to top £1bn in the coming months.
Banks are cautiously funding the struggling contractor on the promise of achieving a £300m disposals programme and cutting costs to the bone.
Davies joined Wates just over three-years ago to turn the private building firm’s fortunes around and double its size from a £1bn to £2bn revenue business.
This remains work in progress with Wates hitting £1.5bn turnover last year.
Prior to that he held a series of senior roles with BAE Systems over a 28 year period.
Carillion chairman Philip Green said Davies brought strategic, turn around and leadership skills to Carillion as well as experience of complex public sector contracting in projects, support services and construction.
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.
“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.”
At Wates, chief financial office David Allen will become acting chief executive when Davies steps down on 10 November pending the appointment of a permanent successor.
Chairman James Wates CBE, said: “When Andrew leaves, he will do so with the company in a strong position and well on its way to achieving its strategic goal of becoming a sustainably profitable £2bn turnover company.
“It’s been a pleasure to work with Andrew over these past four years, and I have thanked him for his outstanding leadership in growing the business, building a strong management team, and ingraining our core values throughout the organisation.”