Igneous bodies are built incrementally by episodic magma injection events that vary in rate and duration. Such recharge events can either grow an upper crustal magma reservoir or trigger an eruption. This bifurcation in behavior remains poorly constrained but is essential to volcanic hazard assessment. Here we use a numerical model that couples the thermal and mechanical processes in a magma reservoir to study the evolution of the Santorini magmatic system (Greece) over the past 20 k.y. Our results constrain the recharge rate and duration that are necessary to trigger an eruption for the known long-term average inflow rate of 10−3 km3/yr. The size of the chamber and its exsolved volatile content are dominant controls on the critical recharge rate and duration that will trigger an eruption. Our model successfully reproduces the main features of the Minoan eruption and Nea Kameni activity, providing volume estimates for the active part of the current subvolcanic reservoir as well as information regarding the presence of exsolved volatiles. Thermomechanical models offer a new framework to integrate the historic eruption record with geodetic measurements and provide a context to understand the past, present, and future of active volcanic centers.