The council declared the Hythe Centre surplus to requirements in June, and discussions have since taken place to convert it into a healthcare centre.
The council said better health facilities “outweighs the Hythe Centre’s value as a hall for hire”.
The new facility is to be about four times the size of the current surgery, with eight consulting and clinical rooms, as well as office space.
The adjacent Hythe Playing Field will not be included in the sale.
A council spokesperson said: “We’re focused on creating an environment that supports the health and wellbeing of local people.
“In this case we can do that by providing the space for an up-to-date medical practice where patients feel confident of great care and medical staff can work at their best in modern conditions.”
An information event about the plans will take place on 13 August at the Hythe Centre, from 14:30 to 18:30 BST.