Accurate global river discharge estimation is crucial for advancing our scientific understanding of the global water cycle and supporting various downstream applications. In recent years, data-driven machine learning models, particularly the Long Short-Term Memory (LSTM) model, have shown significant promise in estimating discharge. Despite this, the applicability of LSTM models for global river discharge estimation remains largely unexplored. In this study, we diverge from the conventional basin-lumped LSTM modeling in limited basins. For the first time, we apply an LSTM on a global 0.25° grid, coupling it with a river routing model to estimate river discharge for every river reach worldwide. We rigorously evaluate the performance over 5332 evaluation gauges globally for the period 2000-2020, separate from the training basins and period. The grid-scale LSTM model effectively captures the rainfall-runoff behavior, reproducing global river discharge with high accuracy and achieving a median Kling-Gupta Efficiency (KGE) of 0.563. It outperforms an extensively bias-corrected and calibrated benchmark simulation based on the Variable Infiltration Capacity (VIC) model, which achieved a median KGE of 0.466. Using the global grid-scale LSTM model, we develop an improved global reach-level daily discharge dataset spanning 1980 to 2020, named GRADES-hydroDL. This dataset is anticipated to be useful for a myriad of applications, including providing prior information for the Surface Water and Ocean Topography (SWOT) satellite mission. The dataset is openly available via Globus.