Using daily data on vaccinations, disease spread and measures of social interaction from Google Mobility reports aggregated at the country level for 112 countries, we present estimates of behavioural responses to the global rollout of COVID-19 vaccines. We first estimate correlates of the timing and intensity of the vaccination rollout, finding that countries which vaccinated more of their population earlier strongly tended to be richer, whereas measures of the state of pandemic or its death toll up to the time of the initial vaccine rollout had little predictive ability after controlling for income. Estimates of models of social distancing and disease spread suggest that countries which vaccinated more quickly also experienced decreases in some measures of social distancing, yet also lower incidence of disease, and in these countries, policy-makers relaxed social distancing measures relative to countries which rolled out vaccinations more slowly.