The 84,000sq ft courtyard building is centrally located and will provide 342 high quality studio rooms with ancillary space.
Acquisitions Director Sam Jefferson said: “We are rolling out the Study Inn brand throughout the UK and Cambridge is a very important addition to our existing room stock.
“We are very pleased to have secured a long leasehold of this very well-located property and its completion will take our portfolio close to 1,500 rooms. The room styles, communal areas and level of service will be new to the city and this will be a flag ship centre for Study Inn.
Ben Green, of Barker Storey Matthews, agents who acted for the County Council said: “There was very keen interest in this prominent property and we were pleased to be able to structure a transaction which achieved the Council’s aspirations for this important disposal.
Steve Count, Leader of Cambridgeshire County Council, said: “Moving from the Castle Court offices has meant that the Council has been able to unlock a significant revenue stream for the authority to use on providing essential services, while supporting new business in Cambridge, and helping to provide much needed student accommodation.
“The move is part of the County Council’s overall drive to get best value from its assets for the benefit of Cambridgeshire’s tax payers.