We estimate the baryonic (stellar+cold gas) mass function of galaxies in the local universe by assigning a complete sample of Two Micron All Sky Survey and Sloan Digital Sky Survey galaxies a gas fraction based on a statistical sample of the entire population, under the assumption of a universally applicable stellar initial mass function. The baryonic mass function is similar to the stellar mass function at the high-mass end and has a reasonably steep faint-end slope owing to the typically high cold gas fractions and low stellar mass-to-light ratios characteristic of low-mass galaxies. The Schechter function fit parameters are phi*h-3 = 0.0108(6) Mpc-3 log M-1, M*h2 = 5.3(3) × 1010 Msun, and α = -1.21(5), with formal error estimates given in parentheses. We show that the H I and H2 mass functions derived using this indirect route are in agreement with direct estimates, validating our indirect method. Integrating under the baryonic mass function and incorporating all sources of uncertainty, we find that the baryonic (stellar+cold gas) mass density implied by this estimate is Ωcold baryonh = 2.4img1.gif × 10-3, or 8img2.gif% of the big bang nucleosynthesis expectation.