We apply a likelihood analysis to pulsar detections, pulsar upper limits, and diffuse background measurements from the OSSE and EGRET instruments on the Compton Gamma Ray Observatory to constrain the luminosity law for gamma-ray pulsars and some properties of the gamma-ray pulsar population. We find that the dependence of luminosity on spin period and dipole magnetic field is much steeper at OSSE than at EGRET energies (50-200 keV and >100 MeV, respectively), suggesting that different emission mechanisms are responsible for low- and high-energy gamma-ray emission. Incorporating a spin-down model and assuming a pulsar spatial distribution, we estimate the fraction of the Galactic gamma-ray background due to unidentified pulsars and find that pulsars may be an important component of the OSSE diffuse flux but are most likely not important at EGRET energies. Using measurements of the diffuse background flux from these instruments, we are able to place constraints on the braking index, initial spin period, and magnetic field of the Galactic pulsar population and are also able to constrain the pulsar birthrate to be between 1/25 yr–1 and 1/500 yr–1. Our results are based on a large gamma-ray beam, but they do not scale in a simple way with beam size. We estimate that about 20 of the 169 unidentified EGRET sources are probably gamma-ray pulsars. We use our model to predict the pulsar population that will be seen by future gamma-ray instruments and estimate that Gamma Ray Large Area Space Telescope will detect roughly 750 gamma-ray pulsars as steady sources, only 120 of which are currently known radio pulsars.