The Peel Group GP Practice has started moving to its new Albany Road surgery.
Patients will only be able to book urgent appointments today.
The new centre will be open for emergency cases on Monday (28) and will open fully next Tuesday (March 1).
The facility has space for six doctors and three nurses, caring for more than 8,000 patients.
Speaking at the handover of keys to the new practice earlier this month, Health Minister David Anderson said the project's been a long time coming: