Hospice chief executive Ann-Marie Kelly said the award will “future-proof the provision of outstanding palliative and end-of-life care for terminally-ill people in our community”.
She said the new hospice would be a community asset where patients and their loved ones could receive support from its staff and volunteers.
“Flooded with natural light and open-spaces, we are eager to welcome our community and to support terminally-ill people to live with comfort, independence and dignity to the end of their lives,” she said.
Councillor Tony Harwood, cabinet member for planning policy and management, said the hospice provided “invaluable support” to thousands of local people and their families.
He said the funding would help to progress plans for facilities that can meet the community’s needs for many years to come.
The council’s funding award is part of a wider £13.8m package approved by the local authority for projects across the borough.
They include education, healthcare, community facilities, transport improvements and public open space.
Follow BBC Kent on Facebook, external, X, external, and on Instagram, external and listen to BBC Radio Kent on Sounds. Send your story ideas to southeasttoday@bbc.co.uk, external or WhatsApp us on 08081 002250.