Sir John, 75, will take up the role later this year when he steps down from his current role as Chairman of mining giant Anglo American.
In the interim he will “familiarise himself with key projects and clients.”
Laing O’Rourke CEO Ray O’Rourke said: “Sir John has built up an enviable reputation across a range of industrial sectors as a leader in the boardroom, including Chairman at five FTSE100 companies.
“As former President of the Royal Academy of Engineering and a visiting Fellow at Oxford University, he takes a keen interest in the development of engineering technology and talent, a core value of our global business.
“I am excited to work closely with Sir John to make Laing O’Rourke the recognised leader for innovation and excellence in the construction industry.”
Sir John said: “I am honoured to join such a progressive organisation, with compelling future plans.
“A culture of engineering excellence is deeply embedded at Laing O’Rourke.
“I have a deep respect for the organisation that Ray and Des O’Rourke built from scratch over the past 40 years.”