Volcanic calderas are surface depressions formed by roof collapse following evacuation of magma from an underlying reservoir. The mechanisms of caldera formation are debated and predict differences in the evolution of the caldera floor and distinct styles of magma recharge. Here we use a dense, active source, seismic tomography study to reveal the sub-surface physical properties of the Santorini caldera in order to understand caldera formation. We find a ∼3-km-wide, cylindrical low-velocity anomaly in the upper 3 km beneath the north-central portion of the caldera, that lies directly above the pressure source of the 2011-2012 inflation. We interpret this anomaly as a low-density volume caused by excess porosities of between 4% and 28%, with pore spaces filled with hot seawater. Vents that were formed during the first three phases of the 3.6 ka Late Bronze Age (LBA) eruption are located close to the edge of the imaged structure. The correlation between older volcanic vents and the low-velocity anomaly suggests that this feature may be long-lived. We infer that collapse of a limited area of the caldera floor resulted in a high-porosity, low-density cylindrical volume, which formed by either chaotic collapse along reverse faults, wholesale subsidence and infilling with tuffs and ignimbrites, phreatomagmatic fracturing, or a combination of these processes. Phase 4 eruptive vents are located along the margins of the topographic caldera and the velocity structure indicates that coherent down-drop of the wider topographic caldera followed the more limited collapse in the northern caldera. This progressive collapse sequence is consistent with models for multi-stage formation of nested calderas along conjugate reverse and normal faults. The upper crustal density differences inferred from the seismic velocity model predict differences in subsurface gravitational loading that correlate with the location of 2011-2012 edifice inflation. This result supports the hypothesis that sub-surface density anomalies may influence present-day magma recharge events. We postulate that past collapses and the resulting topographical and density variations at Santorini influence magma focusing between eruptive cycles, a feedback process that may be important in other volcanoes.