Using both the polar cap and outer gap models of pulsar gamma-ray emission, the pulsars' contribution to the Galactic gamma-ray emission is derived. A Monte Carlo technique is used to model the Galactic pulsar population, and their contribution to the Galactic gamma-ray emission is found to depend strongly upon their birth properties, which remain controversial. The "standard model" of radio pulsar evolution suggests that the majority of the observed gamma-ray emission originates from radio pulsars. However, other models of the Galactic pulsar population, which have pulsars being born with periods near 0s.5, suggest that the contribution is much smaller. For any model, the majority of this emission arises from pulsars currently unknown as radio pulsars. This result holds for both the polar cap, and outer gap models, and suggests that the pulsar contribution to the Galactic gamma-ray emission might be much higher than previous calculations have suggested. The result can be inverted to place limits upon the Galactic distribution of radio pulsars and their birth properties. If pulsars are the predominant source of Galactic gamma-rays, then their mean initial field strengths and periods must be less-than-or-similar-to 10(12) G and less-than-or-similar-to 20 ms, respectively. Although the number of known pulsars detectable by the Compton Gamma Ray Observatory (Compton) is only expected to be less-than-or-similar-to 10, there may be many more observable as point sources either undetectable as radio pulsars due to beaming effects, or simply below the detection threshold of previous radio pulsar surveys. Deep radio observations of all Compton point sources is therefore recommended. It is found that the millisecond pulsars may also contribute significantly to Galactic gamma-ray emission, although population estimates, and the validity of gamma-ray emission models at millisecond pulsar periods and field strengths require confirmation.