We present a fully consistent catalog of local and global properties of host galaxies of 882 Type Ia supernovae (SNIa) that were selected based on their light-curve properties, spanning the redshift range 0.01<z<1. This catalog corresponds to a preliminary version of the compilation sample and includes Supernova Legacy Survey (SNLS) 5-year data, Sloan Digital Sky Survey (SDSS), and low-redshift surveys. We measured low- and moderate-redshift host galaxy photometry in SDSS stacked and single-epoch images and used spectral energy distribution (SED) fitting techniques to derive host properties such as stellar mass and U-V rest-frame colors; the latter are an indicator of the luminosity-weighted age of the stellar population in a galaxy. We combined these results with high-redshift host photometry from the SNLS survey and thus obtained a consistent catalog of host stellar masses and colors across a wide redshift range. We also estimated the local observed fluxes at the supernova location within a proper distance radius of 3kpc, corresponding to the SNLS imaging resolution, and transposed them into local U-V rest-frame colors. This is the first time that local environments surrounding SNIa have been measured at redshifts spanning the entire Hubble diagram. Selecting SNIa based on host photometry quality, we then performed cosmological fits using local color as a third standardization variable, for which we split the sample at the median value. We find a local color step significance of -0.091+/-0.013mag (7{sigma}), which effect is as significant as the maximum mass step effect. This indicates that the remaining luminosity variations in SNIa samples can be reduced with a third standardization variable that takes the environment into account. Correcting for the maximum mass step correction of -0.094+/-0.013mag, we find a local color effect of -0.057+/-0.012mag (5{sigma}), which shows that additional information is provided by the close environment of SNIa. Departures from the initial choices were investigated and showed that the local color effect is still present, although less pronounced. We discuss the possible implications for cosmology and find that using the local color in place of the stellar mass results in a change in the measured value of the dark energy equation-of-state parameter of 0.6%. Standardization using local U-V color in addition to stretch and color reduces the total dispersion in the Hubble diagram from 0.15 to 0.14mag. This will be of tremendous importance for the forthcoming SNIa surveys, and in particular for the Large Synoptic Survey Telescope (LSST), for which uncertainties on the dark energy equation of state will be comparable to the effects reported here.