Many scientific goals for the Dark Energy Survey (DES) require calibration of optical/NIR broadband \(b = grizY\) photometry that is stable in time and uniform over the celestial sky to one percent or better. It is also necessary to limit to similar accuracy systematic uncertainty in the calibrated broadband magnitudes due to uncertainty in the spectrum of the source. Here we present a "Forward Global Calibration Method (FGCM)" for photometric calibration of the DES, and we present results of its application to the first three years of the survey (Y3A1). The FGCM combines data taken with auxiliary instrumentation at the observatory with data from the broad-band survey imaging itself and models of the instrument and atmosphere to estimate the spatial- and time-dependence of the passbands of individual DES survey exposures. "Standard" passbands are chosen that are typical of the passbands encountered during the survey. The passband of any individual observation is combined with an estimate of the source spectral shape to yield a magnitude \(m_b^{\mathrm{std}}\) in the standard system. This "chromatic correction" to the standard system is necessary to achieve sub-percent calibrations. The FGCM achieves reproducible and stable photometric calibration of standard magnitudes \(m_b^{\mathrm{std}}\) of stellar sources over the multi-year Y3A1 data sample with residual random calibration errors of \(\sigma=5-6\,\mathrm{mmag}\) per exposure. The accuracy of the calibration is uniform across the \(5000\,\mathrm{deg}^2\) DES footprint to within \(\sigma=7\,\mathrm{mmag}\). The systematic uncertainties of magnitudes in the standard system due to the spectra of sources are less than \(5\,\mathrm{mmag}\) for main sequence stars with \(0.5<g-i<3.0\).