To combat the public health crisis of Covid-19, governments and public health officials have been asking individuals to substantially change their behaviours for prolonged periods of time. Are happier people more willing to comply with such measures? Using three independent, large-scale surveys covering about 119,000 adult respondents across 35 countries, including longitudinal data from the UK, we find that past and present life satisfaction predicts compliance with preventive health behaviours during Covid-19 lockdowns. The association is stronger for those with higher levels of life satisfaction. A loss in life satisfaction, on the contrary, predicts lower compliance. We explore risk-avoidance and pro-social motivations for this relationship, and find suggestive evidence that people who are older or have certain medical preconditions seem to be behave in line with risk-avoidance, whereas motivations of people who are less at risk of Covid-19 seem more mixed. Overall, our findings indicate that life satisfaction is important, both as a policy end in itself and for complying with new long-term preventive health measures.