Holt said there were existing services running in nearby Sidmouth and Seaton.
Speaking to BBC Radio Devon as part of Wake Up Call – a series encouraging people to check their health, he said: “The £4m we invested in the hospital many years ago left us a bit short of funds in terms of being able to fund this service.
“The service will have special palliative care nurses going into people’s homes where anybody is diagnosed with a life limiting illness of 12 months of less.
“Over the last few years we have significantly fundraised and we now have funds that will ensure that we can support this service for four to five years.”
Holt thanked the community and members of the Axminster Hospital League of Friends for their support.
“This service is required and the people of Axminster deserve it,” he added.