The five connected blocks, ranging from eight to 13 storeys, will be constructed on the former Mecca Bingo site, opposite John Lewis.
Planning officials gave the project the green light despite protests from the insurers Aviva, who are situated close by, arguing that it would negatively impact the working conditions of its employees.
In addition, although the insurers supported the development of the site it was argued that the planned height of the building was excessive and that it should be reduced to 11 storeys.
According to councillor Keith Driver however, an extra two or three storeys are not expected to make much difference to the buildings impact on the area.
Expectations are that the flats will be opened by 2018, although it's unclear at this stage at to which university students in the accommodation would be studying at.
The site will consist of a series of five and eight en-suite flats with shared kitchen facilities. The development will also come with a two-storey communal area.