The project forms part of the council's plans to reduce emissions and protect residents from the effects of climate change.
The underground network will consist of large air source heat pumps, which take heat from the air and use it to warm buildings and water, providing a lower-carbon alternative to conventional heating systems.
The council estimates that the scheme will save more than 100,000 tonnes of carbon dioxide equivalent (CO2e) over the next 40 years when compared with the previous design, which relied on combined heat and power technology alongside gas boilers.
The heat network is one of more than 300 actions included in the council's Climate Implementation Plan, which aims to reduce emissions while delivering practical benefits for residents, including warmer homes, better access to green spaces and improved resilience to climate change.