The OSSE instrument on the Compton Gamma Ray Observatory (CGRO) was used to measure the one-dimensional latitudinal and longitudinal distributions of positron annihilation radiation (annihilation line and positronium continuum components) along the inner Galactic ridge. Intensity measurements near the Galactic center (differential relative to background fields offset by 9 degrees -12 degrees) show a symmetrical and spatially narrow bulge around the center (effective FWHMs of 4.degrees9 +/-0.degrees7 in Galactic latitude and 6.degrees3 +/-1.degrees5 in longitude) with significant disk contributions to at least 35 degrees in longitude. The latitude width of the Galactic plane emission away from the Galactic center is only weakly constrained in the current analysis. The longitudinal distribution is well fitted by either a model comprising a narrow (similar to6.degrees3 FWHM) Gaussian bulge plus similar to 35 degrees FWHM Gaussian and CO-like disk components, or by a center-truncated R(1/4) spheroid plus exponential disk model. For the latter model, the observed narrow latitudinal distribution near the Galactic center suggests that the bulge is ellipsoidal, although the fits are consistent with a spherical bulge as well. The positronium fraction estimate from the Galactic center direction is 0.93 +/-0.04. This, combined with the existing narrow line width measurements for the 511 keV annihilation line, suggests that the bulk of the positron annihilation from the Galactic center direction occurs after positronium formation in a warm environment. The inner Galaxy total annihilation radiation flux intensities of similar to 10.6 x 10(-3) to similar to 13.7 x 10(-3) cm(-2) s(-1) implied by the fitted R(1/4) ellipsoid plus exponential disk model (narrow and broad disks, respectively) are in agreement with intensities implied by the 511 keV line flux observed by the broad-field SMM instrument. The double-Gaussian plus CO disk model gives similar agreement if a broad (similar to 12 degrees FWHM) disk component is assumed.