Jeffries will become chairman, after Sir Alan Rudge retires.
He said the move reflected the firm's continuing commitment to technical services and integrated solutions. While chief executive, Jeffries' main aim was to expand into the USA and make WS Atkins a one-stop services shop.
WS Atkins has undergone a number of board changes in recent years, losing five directors. Its executive board consists of the chief executive and finance director Ric Piper, and has led to criticism that power is too restricted.