Magnetospheric substorms explosively release solar wind energy previously stored in Earth's magnetotail, encompassing the entire magnetosphere and producing spectacular auroral displays. It has been unclear whether a substorm is triggered by a disruption of the electrical current flowing across the near-Earth magnetotail, at approximately 10 R(E) (R(E): Earth radius, or 6374 kilometers), or by the process of magnetic reconnection typically seen farther out in the magnetotail, at approximately 20 to 30 R(E). We report on simultaneous measurements in the magnetotail at multiple distances, at the time of substorm onset. Reconnection was observed at 20 R(E), at least 1.5 minutes before auroral intensification, at least 2 minutes before substorm expansion, and about 3 minutes before near-Earth current disruption. These results demonstrate that substorms are likely initiated by tail reconnection.