Space-borne instruments can measure river water surface elevation, slope and width. Remote sensing of river discharge in ungauged basins is far more challenging, however. This work investigates the estimation of river discharge from simulated observations of the forthcoming Surface Water and Ocean Topography (SWOT) satellite mission using a variant of the classical variational data assimilation method "4D-Var". The variational assimilation scheme simultaneously estimates discharge, river bathymetry and bed roughness in the context of a 1.5D full Saint Venant hydraulic model. Algorithms and procedures are developed to apply the method to fully ungauged basins. The method was tested on the Po and Sacramento Rivers. The SWOT hydrology simulator was used to produce synthetic SWOT observations at each overpass time by simulating the interaction of SWOT radar measurements with the river water surface and nearby land surface topography at a scale of approximately 1 m, thus accounting for layover, thermal noise and other effects. SWOT data products were synthesized by vectorizing the simulated radar returns, leading to height and width estimates at 200 m increments along the river centerlines. The ingestion of simulated SWOT data generally led to local improvements on prior bathymetry and roughness estimates which allowed the prediction of river discharge at the overpass times with relative root-mean-squared errors of 12.1% and 11.2% for the Po and Sacramento rivers respectively. Nevertheless, equifinality issues that arise from the simultaneous estimation of bed elevation and roughness may prevent their use for different applications, other than discharge estimation through the presented framework.