Timing observations of millisecond pulsars PSR J2019 + 2425 and PSR J2322 + 2057 made over more than 2 years have yielded spin-down, astrometric, and binary parameters. The proper motions of these sources are 23.5 +/- 1.3 and 25 +/- 3 mas yr-1, respectively, corresponding to transverse velocities of approximately 100 and 90 km s-1. These measurements, combined with other published millisecond pulsar proper motions, indicate that the population has a velocity dispersion of order 60 km s-1, comparable to that of low-mass X-ray binaries (from which millisecond pulsars evolve) but much lower than that of normal (nonmillisecond) pulsars. The spindown rates of J2019 + 2425 and J2322 + 2057 are extraordinarily low and, when biases induced by motion are removed, formal calculations yield ages of 27 x 10(9) and 19 x 10(9) yr, respectively, indicating they have evolved little since becoming millisecond pulsars.