She starts on 15th September. Current incumbent Duncan Harper will stay on for a month to hand over.
Ms Wright has more than 25 years finance experience within construction and engineering firms, including 16 years at Mowlem plc before joining Midas Group in 2005 as group finance director.
She moved to CH2M Hill in 2006 as commercial and financial director Europe, becoming international commercial director in 2013.
Aukett Swanke chief executive Nicholas Thompson said: "We are delighted to welcome Beverley to the board. She brings a wealth of commercial experience to Aukett Swanke along with significant financial expertise both in the UK and internationally. Beverley will be a valuable addition to the executive team as we pursue our growth objectives. "