The origin of the isotropic gamma-ray background ( IGRB ) — the portion of the extragalactic gamma-ray sky that is not resolvable into individual point sources — provides a powerful probe into the evolution of the high-energy universe . Star-forming galaxies ( SFGs ) are among the most likely contributors to the IGRB , though their contribution is difficult to constrain because their flux distribution is dominated by numerous faint sources . We produce a novel joint-likelihood analysis of the \gamma -ray emission from 584 SFGs , utilizing advanced statistical techniques to compare the distribution of low-significance excesses against the non-Poissonian \gamma -ray background fluctuations . We first examine the theoretically well-motivated relationship between the far-IR and \gamma -ray luminosities of SFGs , utilizing a model where the \gamma -ray luminosity is given by log _ { 10 } ( L _ { \gamma } / ( erg s ^ { -1 } ) ) = \alpha log _ { 10 } ( L _ { IR } / ( 10 ^ { 10 } L _ { \odot } ) ) + \beta . We calculate best-fit parameters \alpha = 1.18 \pm 0.15 , \beta = 38.49 \pm 0.24 , with a log-normal dispersion in this relationship given by \sigma = 0.39 \pm 0.12 . The best-fit values of \alpha and \beta are consistent with previous studies . We find a larger dispersion in the far-IR to \gamma -ray correlation than previous studies . This dispersion is significant at the level of 5.7 \sigma . These results imply that SFGs significantly contribute to the IGRB , producing between 61.0 ^ { +30.2 } _ { -18.3 } \% of the total IGRB intensity above an energy of 1 GeV . Along with recent works , this strongly indicates that multiple source classes provide comparable contributions to the IGRB intensity . We discuss the implication of these results for the interpretation of the IceCube neutrinos .