About 30 Forbush-type decreases occurring from 1972 at 1 AU for which data were available from the IMP spacecraft (P median of ~1.7 GV) and the Mt. Washington neutron monitor (P median of ~5 GV) were examined to determine the characteristic recovery times of the events. The characteristic recovery time t0 was found to be the same for rigidities of ~1.7 GV and ~5.0 GV. Characteristic recovery times for additional Forbush decreases, including some in 1957-1963, were determined, using the Mt. Washington neutron monitor and monitors at cutoff rigidities of ~12 GV, ans were also found to be the same. Hence the characteristic recovery time of Forbush decreases at 1 AU is independent of energy (or rigidity) over a factor of at least 10. The average recovery time t0 at 1 AU is ~5 days but varies from ~3 to ~10 days, and the recovery in most cases is well represented by an exponential. No significant difference in the average recovery time is observed when the solar magnetic field reversed in 1980 nor during the decrease and recovery portion of the solar modulation cycle. A physical model is proposed to explain these results.