Abstract Global food demand is rising, pushed by growing world population and dietary changes in developing countries. This encourages farmers to increase crop production which, in turn, increases worldwide demand for agricultural land and the pressure on tropical forests. With a possible doubling of world food demand by 2050, this pressure is not likely to decrease in the next decades. While the impact of food demand on deforestation has been pushed forward in the medias, rigorous evidence using large-N data estimating the causal impact of crop price variations on deforestation remains scarce. Here, we quantify this impact over the twenty first century using high resolution annual forest loss data across the tropics, combined with information about crop-specific agricultural suitability and annual international commodity prices. We find a sizeable impact of price variations on deforestation: crop price variations are estimated to have contributed to 35% of the total predicted deforestation in the tropics over the period 2001-2018. We also highlight that the degree of openness to international trade and level of economic development are first-order local characteristics to explain the magnitude of the impact of crop prices on deforestation.