Satellite-based precipitation products (SPPs) with short latencies provide a new opportunity for flood forecasting in ungauged basins. However, the larger uncertainties associated with such near-real-time SPPs can influence the accuracy of the resulting flood forecast. Here we propose a real-time updating method, referred to as “Constrained Runoff Correction (CRC-M)” that is based on the use of multi-source SPPs. The method is based on the hypothesis that the range over different near-real-time SPPs provides insight regarding the approximate range in which the true rainfall value lies, during the current period. Accordingly, the constrained runoff correction is performed in such a way as to be consistent with this range, and with the observed value of discharge at the basin outlet. Evaluation using real-data indicates that the new method performs well, with Nash–Sutcliffe (NS) values of 0.85 and 0.91 during calibration and evaluation, respectively. The necessity and value of imposing constraints is demonstrated by comparing CRC-M against a control, referred to as “Unconstrained Runoff Correction” (URC-S). Experiments indicate that the key factors resulting in good performance are 1) wider constraint ranges, and 2) relatively reliable SPPs. Further, inclusion of redundant information may only result in slight improvements to forecast performance, and can even cause the performance to deteriorate. Overall, the CRC-M method can result in accurate and stable flood forecasts for ungauged basins, without the need for increased model complexity (i.e., the numbers of model parameters).