Mayflower Manhattan Limited has had its application for 35 studios and two single-bedroom flats at Adam Court in Newark Road, Fengate, accepted by Peterborough City Council.
This was the second time plans for the site had been submitted after the council had rejected an earlier application due to noise concerns for residents who would move in.
According to the latest proposals, three of the office buildings at Adam Court - which was constructed in 1990 - will be converted into residential use, with 46 parking spaces retained and a cycle shelter installed.
The Cambridge-based firm said the offices are “at present largely unoccupied with only two short-term tenancies”.
Its application to the council added: “The proposal seeks to offer a significant and growing sector of the housing market in the UK - single person households - with high quality self-contained homes at attainable rents.
“By replacing office space in low demand with much needed residential accommodation that is close to a wide range of employment opportunities, we consider that the proposal supports the wider aspirations of the Local Plan to promote and develop the Peterborough economy.”