A site in Kirkintilloch in East Dunbartonshire is also closing.
The move comes as some centres – which were initially mobilised to cohort and care exclusively for Covid-19 patients – have seen just a handful of attendances per day in the last week, with numbers continuing to fall across sites.
However, both centres can be rapidly remobilised should they be required.
Similar to other health centres across Greater Glasgow and Clyde, Eastwood and Kirkintilloch Health centres will continue to provide a range of services as the health service moves into recovery from Covid-19.
Moving forward, the CAC service will be run from the remaining core centres – Barr Street in Glasgow, Greenock Health Centre, Linwood Health Centre, Renton Integrated Healthy Living Centre and Clydebank Health Centre.
Patients in East Renfrewshire will be asked to attend their nearest centre and NHSGGC’s patient transport service will take patients to and from their appointments if required.
NHSGGC’s CACs were mobilised at the beginning of the pandemic to provide a streamlined pathway for patients who had Covid-19 symptoms to ensure they received the most appropriate care as quickly as possible.
The seven specialist centres played a central role in effectively cohorting patients and protecting other primary and acute care services from being overwhelmed as well as the safety of patients and staff.
To date more than 5500 patients have been through the centres.
Dr Jim O’Neil, lead clinician at Barr Street Community Assessment Centre in Glasgow, said: “It’s great news to be able to wind down two of our CACs as it means community transmission is reducing across Greater Glasgow and Clyde in line with the rest of Scotland.
“Staff who had been redeployed to the CACs can move back into other roles as we adapt into a recovery phase to allow us to scale back up services which have been impacted by the pandemic.
“The CACs were designed to serve a short-life span and have been very effective in helping treat people with COVID-19 symptoms throughout the pandemic. However, numbers have been steadily declining and in line with planning, services have been reduced to meet falling demand.
“We have retained a full service across other sites and we will continue to review the situation on a daily basis to inform and allow us to scale back up, if required.
“We’d like to thank all the staff involved in helping mobilise and run the CACs so effectively and in such a short space of time.”