In all, four land transactions and the school sale are expected to be approved by the council today in a deal worth almost £800,000.
The land is surplus from the creation of a major new road through the east end and had at first been offered to a local housing association and regeneration agency who did not take up the offer.
A wing of the HM Revenue and Customs, the District Valuer Services (DVS), came up with the price Celtic will pay.
The sale of the London Road Primary, which will be demolished, will be for around £360,000.
However, there will be caveats, with the DVS insisting "the council should seek to bind the parties to a programme of environmental improvements in view of the forthcoming Commonwealth Games".
If Celtic use the land for anything beyond a superstore or ticket office within the next 15 years the council will receive a further £100,000.
There had also been heritage issues around the school but last night Historic Scotland said: "It is disappointing that the B-listed former London Road Primary could not be incorporated into the plans for the 2014 Commonwealth Games.
"However we took into account all the circumstances of the case and referred the case back to Glasgow City Council for their own decision."