COVID-19 is the most critical health and safety risk facing the global construction sector. The COVID-19 crisis leads to a reduction in site productivity, has increased compliance costs, delayed projects and increased construction workers' exposure to risk and infections. However, as countries begin to ease lockdowns and restrictions, there is a need to examine the measures that the construction companies can take to ensure workers are "Covid-safe". This research developed a questionnaire instrument that included 24 Covid-preventive measures on construction sites. Isolating sick workers, conducting daily checks for COVID-19 symptoms, preventing hugging/handshaking at the site, displaying health advisory posters and info-graphics, and providing face masks to workers are seen to be the main measures towards keeping sites "Covid-safe". The Principal Component Analysis structured the 24 measures into 4 components. The 4 components explained about 73% of the model, namely hygiene and control, equipment and monitoring, awareness, and incentives. The results found that compliance costs of health and safety regulations to prevent COVID-19 will increase project cost by more than 20%, site productivity will be reduced by up to 50%, and the pandemic will have caused a 40% increase in skill shortages. Cluster analysis was performed to cluster the sites in terms of their exposure to COVID-19 risk. In order to examine the practicability of the findings, the model was validated with 4 case studies. It is asserted that the research findings have the potential to keep sites "Covid-safe", which helps construction companies increase productivity, reduce project costs, reduce claims, and deliver projects on schedule. This research is the first to examine measures to prevent the spread of COVID-19 on construction sites, and the findings hold critical theoretical and practical implications for future research on health and safety management.