Two- and three-dimensional particle-in-cell simulations are used to determine the mechanism for producing relativistic electrons during externally driven magnetic reconnection in a plasma sheet configuration that models the near-Earth growth phase magnetotail. The dominant process is found to be of the inverse Landau-damping type in which those electrons with velocity component vx ≈ 0 at the X line are accelerated across the tail by the inductive reconnection electric field Ey. This process produces a power-law energy spectrum for the electrons with a slope of ~5--6, in agreement with recent observations.