In response to the outbreak of the coronavirus disease 2019 (Covid-19), governments worldwide have introduced multiple restriction policies, known as non-pharmaceutical interventions (NPIs). However, the relative impact of control measures and the long-term causal contribution of each NPI are still a topic of debate. We present a method to rigorously study the effectiveness of interventions on the rate of the time-varying reproduction number Rt and on human mobility, considered here as a proxy measure of policy adherence and social distancing. We frame our model using a causal inference approach to quantify the impact of five governmental interventions introduced until June 2020 to control the outbreak in 113 countries: confinement, school closure, mask wearing, cultural closure, and work restrictions. Our results indicate that mobility changes are more accurately predicted when compared to reproduction number. All NPIs, except for mask wearing, significantly affected human mobility trends. From these, schools and cultural closure mandates showed the largest effect on social distancing. We also found that closing schools, issuing face mask usage, and work-from-home mandates also caused a persistent reduction on Rt after their initiation, which was not observed with the other social distancing measures. Our results are robust and consistent across different model specifications and can shed more light on the impact of individual NPIs.