Sheffield suddenly left Laing O’Rourke after three years at the private construction group, first as director of the European Hub and more recently managing director of construction.
He joined the business from Kier, where he rose through the ranks to become chief executive over a 31-year career with the business.
Sheffield will join BAM at the end of August after existing chairman Peter Elverding retired for health reasons and was replaced by Harrie Noy creating a vacancy.
He will serve the board until 2021.
The UK construction market has developed to become BAM’s second biggest home market in recent years.
Since 2015, Sheffield has also been a non-executive director of Southern Water Services, which offers water supply and wastewater services for Kent, Sussex, Hampshire and the Isle of Wight.