The new connection will serve 375 new homes in the Castle Park View housing development once the building is completed in 2022.
Castle Park View is a 26-storey tower block being developed by Bouygues’ Linkcity division. Bouygues UK is main contractor for the project.
The council's existing heat networks connect more than 1,000 social housing properties but this will be first commercial connection to a privately developed site, generating an income for the council.
Councillor Kye Dudd, cabinet member for energy and transport said: "We're in discussions with a number of new developers in the city centre and with supportive planning conditions in place we have high hopes that this connection will be the first of many."