The programme will help the council to reduce its carbon footprint by making changes to 14 of its buildings, such as moving over to heat pumps rather than relying on fossil fuels to run their heating systems.
The work has been split into four Lots, with contracts totalling £2.15m being awarded to CBG Construction Ltd to carry out the work on Lots 1 and 2.
More than £834,000 will be spent on the fire stations in East Grinstead, East Wittering and Petworth, while a further £1.315m will be spent on the libraries in Crawley, Durrington and Southwick.
A budget of just over £7.9m was approved for the first phase of the heat decarbonisation programme, £1.38m of which came from a government grant.
A decision is still to be made about who will carry out the work needed for the remaining two Lots.
Lot 3 will cover Glebelands Day Centre, in Shoreham-by-Sea, and the fire stations in Haywards Heath, Midhurst and Steyning.
Lot 4 will cover the libraries in Broadfield, Haywards Heath and Storrington.