Are well-functioning institutions and local voluntary cooperation substitutes or complements? In a large-scale experimental data set spanning more than 40 diverse societies, we show that higher levels of voluntary cooperation in public goods games without and with punishment are positively associated with societies’ quality of institutions. Through laboratory experiments, we provide causal evidence that experiencing well-functioning institutions subsequently increases voluntary cooperation—even in the absence of formal enforcement mechanisms. Cooperative beliefs – enhanced by the experience of well-functioning institutions – are a crucial behavioural channel contributing to the observed spillover from formal institutions to voluntary cooperation.