Conservation agriculture (CA) is being promoted as a set of management practices that can sustain crop production while providing positive environmental benefits. However, its impact on crop productivity is hotly debated, and how this productivity will be affected by climate change remains uncertain. Here we compare the productivity of CA systems and their variants on the basis of no tillage versus conventional tillage systems for eight major crop species under current and future climate conditions using a probabilistic machine-learning approach at the global scale. We reveal large differences in the probability of yield gains with CA across crop types, agricultural management practices, climate zones and geographical regions. For most crops, CA performed better in continental, dry and temperate regions than in tropical ones. Under future climate conditions, the performance of CA is expected to mostly increase for maize over its tropical areas, improving the competitiveness of CA for this staple crop.