Understanding the controls for magma ascent and storage depth is important for volcanic hazard assessment. Regional differences in the depths of magma storage between volcanic arcs suggest that the settings of subduction zones and of overriding plates influence how magma ascends through the crust. Here we use a compilation of data for 70 volcanoes in 15 volcanic regions to better understand the geodynamic controls on magma storage. We describe the subduction system, which consists of the subducting slab, the mantle wedge, and the upper plate with 12 parameters encompassing the kinematics of the subduction, the structure and geometry of the slab, the timing of the subduction, the thermal structure of the slab, the upper-plate crustal structure, its stress regimes, and its thermal structure. We find that the magma reservoir depths correlate with the upper-plate crustal structure and with the stress regimes. Shallow reservoirs (<5 km depths) are 52% more common in young Tertiary crust than in old Precambrian crust and 42% more common in thin crust (<25 km) than in thick crust (>45 km). Similarly, shallow magma reservoirs are 33–69% more common in extensional and strike-slip stress regimes that in compressional regimes. This illustrates the effect of buoyancy for magma ascent as well as the importance of stress regime and preexisting structures.