O'Rourke, speaking for the first time since White's departure last week, denied speculation that the relationship between the men had been fraught.
"There was no clash of personalities. Andy had achieved a lot in the five months, and the restructuring I brought him in to do had gone faster than expected," O'Rourke said. "He now wants to set up his own property development company in the North."
He added that White had always considered setting up his own business and had good opportunities around his base in northern England.
White was unavailable for comment because of a family bereavement.
White's departure, announced last Monday, shocked the industry. When O'Rourke poached him from Alfred McAlpine five months ago, he was portrayed as the man who would re-establish Laing as a major force in British contracting.
O'Rourke said White's contract had been for a maximum of two years, although he conceded that he had not expected him to leave so soon.
He added that White had in fact been working for O'Rourke for longer than five months.
O'Rourke revealed that the deal with McAlpine had allowed White to work part time for his company since November last year, rather than May as previously thought.
Building had revealed that White had continued to work for McAlpine after he joined O'Rourke – an arrangement that caused much surprise in the industry.
O'Rourke refused to be drawn on his plans to appoint White's replacement, but did confirm that he was not currently seeking an external candidate. "We have a lot of talented people within the group," he said.
Despite O'Rourke's claims, industry sources said White had found it hard to work for O'Rourke, who keeps a close watch on all facets of his business.
One source close to Laing O'Rourke said: "He's trying to run the group like he ran the concrete business, and it's not working. White has a good reputation and his leaving will not help O'Rourke."
O'Rourke confirmed that Grant McGregor, the commercial director of the group's concrete division, was also leaving. He is rejoining Sir Robert McAlpine, which he left last year.