The contractor's chairman, Andrew Wates, will be acting as executive chairman until a new CEO is appointed.
Wates said that Robertson had brought drive, commitment and transparency to the company.
He said: "Beyond the impressive financials, in the past few years Wates has become one of the safest major contractors in the UK and staff turnover has been reduced from 27% to 10%." Robertson is not expected to seek another full-time role and will instead concentrate on his portfolio of non-executive directorships as well spending more time at home.
Wates added that the company's board was now researching the most appropriate firm to use to headhunt Robertson's successor.
He said: "We have not yet decided whether we will be appointing an internal or external person for the job."
He added, however, that the group's structure and strategy would remain the same and that the company would continue to have three regional managing directors.
We have not yet decided whether to appoint an external or internal person
Andrew Wates, chairman
Andrew Wates also ruled out that the move was a sign that the Wates family was planning to regain control of the company.
Under Robertson's stewardship, the contractor promised a 35% improvement in its safety record and aimed to double the turnover of its housing business to £100m by 2008. The company also intends to introduce more and better off-site manufacturing methods.
The Wates Group has three divisions dealing with the private sector, the public sector and the residential sector. These are headed by managing directors Martin Tidd, Dave Smith and Paul Phipps.
Robertson announced last July that he expected group turnover to increase to about £600m this year, compared with £504.5m last year.