We present catalogues of stellar masses, star formation rates, and ancillary stellar population parameters for galaxies spanning $0<z<9$ from the Deep Extragalactic VIsible Legacy Survey (DEVILS). DEVILS is a deep spectroscopic redshift survey with very high completeness, covering several premier deep fields including COSMOS (D10). Our stellar mass and star formation rate estimates are self-consistently derived using the spectral energy distribution (SED) modelling code ProSpect, using well-motivated parameterisations for dust attenuation, star formation histories, and metallicity evolution. We show how these improvements, and especially our physically motivated assumptions about metallicity evolution, have an appreciable systematic effect on the inferred stellar masses, at the level of $sim$,0.2 dex. To illustrate the scientific value of these data, we map the evolving galaxy stellar mass function (SMF) and the SFR-$M_star$ relation for $0<z<4.25$. In agreement with past studies, we find that most of the evolution in the SMF is driven by the characteristic density parameter, with little evolution in the characteristic mass and low-mass slopes. Where the SFR-$M_star$ relation is indistinguishable from a power-law at $z>2.6$, we see evidence of a bend in the relation at low redshifts ($z<0.45$). This suggests evolution in both the normalisation and shape of the SFR-$M_star$ relation since cosmic noon. It is significant that we only clearly see this bend when combining our new DEVILS measurements with consistently derived values for lower redshift galaxies from the Galaxy And Mass Assembly (GAMA) survey: this shows the power of having consistent treatment for galaxies at all redshifts.
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