Based on sensitive CO measurements from HERACLES and HI data from THINGS, we show that the azimuthally averaged radial distribution of the neutral gas surface density (Sigma_HI + Sigma_H2) in 33 nearby spiral galaxies exhibits a well-constrained universal exponential distribution beyond 0.2*r25 (inside of which the scatter is large) with less than a factor of two scatter out to two optical radii r25. Scaling the radius to r25 and the total gas surface density to the surface density at the transition radius, i.e., where Sigma_HI and Sigma_H2 are equal, as well as removing galaxies that are interacting with their environment, yields a tightly constrained exponential fit with average scale length 0.61+-0.06 r25. In this case, the scatter reduces to less than 40% across the optical disks (and remains below a factor of two at larger radii). We show that the tight exponential distribution of neutral gas implies that the total neutral gas mass of nearby disk galaxies depends primarily on the size of the stellar disk (influenced to some degree by the great variability of Sigma_H2 inside 0.2*r25). The derived prescription predicts the total gas mass in our sub-sample of 17 non-interacting disk galaxies to within a factor of two. Given the short timescale over which star formation depletes the H2 content of these galaxies and the large range of r25 in our sample, there appears to be some mechanism leading to these largely self-similar radial gas distributions in nearby disk galaxies.
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