Neutrinoless double beta decay (0νββ) is a yet unobserved nuclear process that would demonstrate Lepton number violation, a clear evidence of beyond standard model physics. The process two neutrino double beta decay (2νββ) is allowed by the standard model and has been measured in numerous experiments. In this Letter, we report a measurement of 2νββ decay half-life of ^{100}Mo to the ground state of ^{100}Ru of 7.07±0.02(stat)±0.11(syst)×10^{18}  yr by the CUPID-Mo experiment. With a relative precision of ±1.6% this is the most precise measurement to date of a 2νββ decay rate in ^{100}Mo. In addition, we constrain higher-order corrections to the spectral shape, which provides complementary nuclear structure information. We report a novel measurement of the shape factor ξ_{3,1}=0.45±0.03(stat)±0.05(syst) based on a constraint on the ratio of higher-order terms from theory, which can be reliably calculated. This is compared to theoretical predictions for different nuclear models. We also extract the first value for the effective axial vector coupling constant obtained from a spectral shape study of 2νββ decay.