David Stewart has made the move following a media storm in Australia relating to allegations of corruption at his previous employer Leighton Holdings.
O’Rourke said: “Mr Stewart has decided that by resigning his position now he can concentrate exclusively on addressing these allegations without the risk of causing damage to Laing O’Rourke’s reputation.”
Stewart joined O’Rourke in May 2012 following 25 years at Leighton where he rose to become chief executive officer.
Stewart will be replaced by Cathal O’Rourke as managing director of Laing O’Rourke’s Australian business and a member of the Group Executive Committee.
Laing O’Rourke Group Chief Executive, Anna Stewart, said: “I am grateful to David for taking the tough decision to step down at this time.
“His action respects the exemplary business values and ethical practices that Laing O’Rourke maintains through its relationships with our clients and stakeholders.
“I am delighted that Cathal has agreed to step up and take the reins of the Australian business having played a major role in its transformation over the last four years.
“His engineering and construction expertise, coupled with an intimate knowledge of our culture and operations, will ensure we continue to develop a strong and thriving business in the region that is able to respond effectively to our clients’ challenges.”