The contractor was picked by developer Olympian Homes for the Hume House tower, which will stand 114 m when completed and provide 278,000 sq ft of accommodation space.
Construction work started this week on the 37-storey building, which will feature 752 bedrooms and create 300 construction jobs at the peak of construction.
The tower will also include a roof terrace on the 35th floor that will serve as a viewing gallery.
Hume House will be one of the biggest projects delivered by Kent-based RG Group, which specialises in residential, commercial and retail buildings.
Other student accommodation projects delivered by RG Group include a 669-room student village in Wembley, the 586-room Staniforth House Tower in Birmingham and the 528-room development in North Lodge student block in London – all of which being delivered for student housing developer Unite Students.
In its latest accounts, RG Group posted turnover of £196m for the 12 months to 31 December 2017, up from £147m for the previous year.
However, the company’s pre-tax profit for 2017 fell to £364,000, down from £1.4m in 2016.
Commenting on the Hume House deal, Olympian Homes chief executive Simon Murray-Twin said: “We awarded the building contract to RG Group on the basis of their expertise, experience and attention to detail.
“We have enjoyed a positive collaboration throughout the tender process to create a building of which we and the city will be proud.”