Time-resolved measurements of spin-transfer-induced (STI) magnetization reversal were made in current-perpendicular spin-valve nanomagnetic junctions subject to a pulsed current bias. These results can be understood within the framework of a Landau-Lifshitz-Gilbert equation that includes STI corrections and a Langevin random field for finite temperature. Comparison of these measurements with model calculations demonstrates that spin-transfer induced excitation is responsible for the observed magnetic reversal in these samples.