As part of the service, food waste containers and one roll of bin liners will be delivered to homes in the district.
There will be a seven-litre caddy for indoor use and a 23-litre bin to be placed on the kerb each week.
The waste which is collected will then be sent to an anaerobic digestion plant to be converted into biofertiliser and renewable energy, the council said.
Woodiwiss added: “By separating food waste, we can ensure it is put to good use, generating renewable energy and valuable biofertiliser, while also supporting our wider environmental and climate objectives.
“We are committed to making this new service as straightforward as possible and will provide the support needed to help households make the most of it.”