The oil and gas services company said yesterday that Mr Murray would leave its board with immediate effect.
It is understood he is leaving for compassionate reasons related to illness in his family.
Petrofac said its senior independent director Rijnhard van Tets, who has been on the board since 2007, will step into the chairman post.
Mr Murray, who has been chairman since 2011, said: "It is with tremendous sadness that I step down from the board. I would like to thank my board colleagues for their support during my tenure and their understanding of my current situation.
"I leave Petrofac in good shape and the board in Rijnhard's experienced and capable hands."
Mr Murray, who trained as accountant after graduating from Heriot-Watt University in Edinburgh, is also chairman of Edrington Group.
It is expected that he will remain in his role at the spirits producer.
He has held a number of board roles during his career, including at pubs group Greene King and milk producer Robert Wiseman Dairies, as well as the chairman role at Cairn Energy.
Prior to taking up a portfolio of non-executive roles, he co-founded Morgan Grenfell Private Equity with his former flatmate Lord Smith of Kelvin in 1989.
Mr Murray also chaired the independent committee charged with establishing the Audit Firm Governance Code, which was published by the Financial Reporting Council in January 2010, and is a past president of the Institute of Chartered Accountants of Scotland.
Petrofac said non-executive Thomas Thune Andersen will become its senior independent director.
Ayman Asfari, group chief executive, said: "I would like to thank Norman for leading the board so effectively for the last three years.
"While it is with great sadness that we accept his resignation, we understand his reasons and our thoughts and best wishes remain with him and his family.
"I am pleased that we have appointed Rijnhard who is an experienced chairman and whose knowledge and understanding of the Petrofac Group will hold us in good stead as we move forward."