The European Centre for Medium-range Weather Forecast (ECMWF) provides an aerosol re-analysis starting from year 2003 for the Monitoring Atmospheric Composition and Climate (MACC) project. The re-analysis assimilates total aerosol optical depth retrieved by the Moderate Resolution Imaging Spectroradiometer (MODIS) to correct for model departures from observed aerosols. The re-analysis therefore combines satellite retrievals with the full spatial coverage of a numerical model. Re-analysed products are used here to estimate the shortwave direct and first indirect radiative forcing of anthropogenic aerosols over the period 2003-2010, using methods previously applied to satellite retrievals of aerosols and clouds. The best estimate of globally-averaged, all-sky direct radiative forcing is -0.5 Wm-2. Accounting for uncertainties in the aerosol anthropogenic fraction, aerosol absorption, and cloudy-sky effects, results in the direct radiative forcing being bounded by -0.8 and 0 Wm-2. Further accounting for differences between the present-day natural and pre-industrial aerosols provides a direct radiative forcing estimate in the range -0.5 to 0 Wm-2, with a best estimate of -0.3 Wm-2. The best estimate of globally-averaged, all-sky first indirect radiative forcing is -0.4 Wm-2. Accounting for uncertainties in the aerosol anthropogenic fraction, cloud albedo, and cloud droplet number concentration susceptibility to aerosol changes, lower and upper bounds of the first indirect radiative forcing are -2.1 Wm-2 and -0.1 Wm-2 In order to decrease uncertainty ranges, better observational constraints on aerosol absorption and susceptibility of cloud droplet number concentrations to aerosol changes are required.