Insidethegames quotes senior sources saying his appointment will be officially announced later today.
It is understood that Robertson will take on the role within the newly hatched Department of Culture, Olympics, Media & Sport, which will be headed by Jeremy Hunt.
First thoughts are that the 47-year-old former Major in the Life Guards has proved a calm, sensible and engaged commentor on Olympic Legacy during his period as Shadow spokesman on Sports and Olympics.
He has unsurprisingly got most heated about a perceived lack of government transparency over taxpayer funding of the Olympics development, particularly when negotiations with the private sector over building the village and media centre were floundering.
It will be interesting to see if he continues to be so committed to openness in this area now.
He has also talked often about how important it is that the project provides real regeneration for east London. Here he is writing about it all last August:
"The major outstanding issue is legacy. It is a worry that neither the main stadium nor the broadcast and media centre have key anchor tenants and there has been little progress on delivering the promise, made when we won the bid, to use London 2012 to reengage young people in sport. This is important for one simple reason. If we transform the area around Stratford but leave no more people enjoying the opportunities available through sport, we will have missed a once in a lifetime opportunity."
That sounds good but is easier to say from the sidelines than to put into practice.
Clearly the uneasy alliance on crucial Olympics decisions between a Tory London mayor and a Labour central government has been extinguished but it remains to be seen how helpful this will be.
It seems certain the Tory Party is going to give Boris greater control over the Olympic Park Legacy Company, something that could significantly change how regeneration is carried out in the area.