The signature of Fe-60 in deep-sea crusts indicates that one or more supernovae exploded in the solar neighbourhood about 2.2 million years ago(1-4). Recent isotopic analysis is consistent with a core-collapse or electron-capture supernova that occurred 60 to 130 parsecs from the Sun(5). Moreover, peculiarities in the cosmic ray spectrum point to a nearby supernova about two million years ago(6). The Local Bubble of hot, diffuse plasma, in which the Solar System is embedded, originated from 14 to 20 supernovae within a moving group, whose surviving members are now in the Scorpius-Centaurus stellar association(7,8). Here we report calculations of the most probable trajectories and masses of the supernova progenitors, and hence their explosion times and sites. The Fe-60 signal arises from two supernovae at distances between 90 and 100 parsecs. The closest occurred 2.3 million years ago at present-day galactic coordinates l = 327 degrees, b = 11 degrees, and the second-closest exploded about 1.5 million years ago at l = 343 degrees, b = 25 degrees, with masses of 9.2 and 8.8 times the solar mass, respectively. The remaining supernovae, which formed the Local Bubble, contribute to a smaller extent because they happened at larger distances and longer ago (Fe-60 has a half-life of 2.6 million years(9,10)). There are uncertainties relating to the nucleosynthesis yields and the loss of Fe-60 during transport, but they do not influence the relative distribution of Fe-60 in the crust layers, and therefore our model reproduces the measured relative abundances very well.