The deal saves the jobs of all 72 remaining staff at the hire unit who transfer to Peterbourough-based Elliott.
Based in Huntly, RB Farquhar Hire turns over about £7m a year providing temporary accommodation including offices, canteens and toilet facilities.
Blair Nimmo of administrator KPMG said: “It is good news that we have now finalised the sale of this business in a little over three months.”
The modular building specialist once supplied bathrooms to the Olympic Village from its prefab factory in the Czech Republic.
But the family-owned Scottish firm last November buckled beneath the weight of the construction downturn and an unsuccessful expansion in the Middle East.
This saw the pod manufacturing arm closed with the loss of 27 UK jobs, but KPMG kept the remaining hire and self-storage parts of the group trading.
KPMG is also negotiating a sale of the self-storage business.