The forthcoming Surface Water and Ocean Topography (SWOT) mission will vastly expand measurements of global rivers, providing critical new datasets for both gaged and ungaged basins. SWOT discharge products will provide discharge for all river reaches wider than 100 m, but at lower accuracy and temporal resolution than what is possible in situ. In this paper, we describe how SWOT discharge produced and archived by the US and French space agencies will be computed from measurements of river water surface elevation, width, and slope and ancillary data, along with expected discharge accuracy. We present here for the first time a complete estimate of SWOT discharge uncertainty budget, with separate terms for random (standard error) and systematic (bias) uncertainty components in river discharge timeseries. We expect that discharge uncertainty will be less than 30% for two thirds of global reaches and will be dominated by bias. Separate river discharge estimates will combine both SWOT and in situ data; these “gage constrained” discharge estimates can be expected to have lower systematic uncertainty. Temporal variations in river discharge timeseries will be dominated by random error and are expected to be estimated to within 15% for nearly all reaches, allowing accurate inference of event flow dynamics globally, including in ungaged basins. We believe this level of accuracy lays the groundwork for SWOT to enable breakthroughs in global hydrologic science.