The 130m high landmark housing scheme is planned by developer AQ Investments, part of the Renaker Build Group of companies, which is also constructing 1,600 apartments across four other sites in the area.
Designed by OMI Architects, work on the 350-flats is now due to start in June for completion in late 2018.
It will be one of a trio of new towers on Trinity Way after Silverlane Development’s 34 and 14 storey Norton Court scheme.
Andy Finch, head of sales at Renaker Build, said: “We are obviously delighted to have obtained the planning consent for this, our latest development and our second within Greengate.
“We are fully committed to the redevelopment of the wider Greengate area and further regeneration and development is planned moving forward.
“Exchange Court has been designed with a broad range of apartment types which will attract a vibrant and diverse range of occupiers, keen to interact with the growing population in the area, creating a sense of place and community.”