Sir Neville, who will become non-executive chairman, said the move had always been planned following Carillion's demerger from Tarmac last year.
The group will now be headed by John McDonough, 49, currently at US facilities management giant Johnson Controls, who takes over the chief executive role in January.
Sir Neville said McDonough's appointment was part of the group's strategy to move into the facilities management and maintenance market.
He said: "They [the City] knew I was going. It was nothing to do with that. You do not find new chief executives in a matter of weeks. You do not pander to rumour."
City sources said the move was in response to losses being discovered at M&E subsidiary Crown House Engineering in the summer, which resulted in 900 redundancies and a £34m exceptional charge.
One source said: "He is carrying the can for Crown House. Those losses should have been accounted for when the Tarmac demerger was completed."
Sir Neville said McDonough, currently vice-president of facilities management for Europe, the Middle East and Africa at Johnson, would bring new ideas to the group.
Sir Neville commented: "We need new blood to drive the business on. It's time for somebody else to put their impetus into the company."
He said it was too early to say whether the group would switch to the support services sector of the stock exchange in line with rivals Amey and Jarvis.
He said: "It's too far in the future to talk about. There will be a balance of earnings between contracting and our services operations in the next year or so. But who knows? By then, contractors may be better rated."
The firm is predicting that its service-related activities will soon contribute half of the firm's operating profit. It has bullish plans to expand its corporate PFI portfolio.
Sir Neville said he was still committed to the group. He said: "I will be here to gear and steer as opposed to push and pull."
The group posted a pre-tax loss of £9.3m for the half-year to 30 June, largely as a result of Crown House's problems. Turnover grew 6% to £926m.