The development, valued at £195m, will provide rooms for 913 students in Middlesex Street in London E1.
It is Unite’s first major development in London since 2013.
The consent remains subject to approval from the Greater London Authority, which is anticipated in the next few weeks, Unite says.
The building will L-shaped, with its main frontage onto the Middlesex Street Gyratory. It would have a mix of 8-storey, 16-storey and 24-storey elements, with the tallest section occupying the southern part of the site.
An existing electricity substation on the site will be demolished and reconstructed within the new building.
The developer is aiming to have it built and ready for students by September 2021.
The planning application has been supported through planning by Kings College London, with both parties working towards a long-term nomination agreement.
Nick Hayes, Unite Students Group property director, said: "London is the UK's largest student market but also one of the most difficult in which to deliver new supply. Middlesex Street creates new supply in a strategically important location where there is a shortage of affordable, high quality accommodation. The scheme adds to our London pipeline, which already includes the 678-bed forward fund development at First Way in Wembley, due for completion in 2020."