The proposals, submitted by Unite Students, will initially become the short-term home of Durham University's St Hild and St Bede.
The longer-term proposals are anticipated to provide the university with a new 18th college.
The development will be improved and upgraded to provide student and staff facilities including college staff offices, welfare, study spaces, and a new building will house common rooms, study areas and a bar.
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A new two-storey amenity hub will be built in front of the current building and external alterations will be carried out in 2024 before being handed over for university use.
Tom Brewerton, Group Development Director at Unite Students, said he is "pleased to be able to support Durham University".
He continued: "It's great that Durham County Council has recognised the benefits of this plan to upgrade Rushford Court. We're proud to be working in partnership with Durham University on this project, which we hope will lead to the creation of a university college. We're pleased to be able to support Durham University in this way and look forward to continuing to work closely together going forward and strengthening our partnership."
