The Agulhas Current (AC) is a critical component of the global ocean circulation. Climate models consistently project the AC to decline in the 21st century. Previous studies typically attributed the weakening of AC to changes in Indian Ocean wind and/or a decline of the Indonesian Throughflow (ITF) transport. However, our analysis suggests that changes in local surface wind and ITF can only explain a portion of the model‐simulated AC changes. Using a hierarchy of models, we show that the decline of the Atlantic Meridional Overturning Circulation (AMOC) strength in a warming climate could also contribute substantially to the AC weakening. Following a weakening of the AMOC, the baroclinic structure of the AC is also modified such that the AC is shoaled to a shallower depth, communicated between basins via Kelvin waves. Our results highlight the importance of remote processes in future western boundary current changes. Plain Language Summary: The Agulhas Current (AC) is one of the strongest currents in the ocean and plays an important role in the climate system. Climate models consistently project a rapid weakening of the AC during the 21st century. Traditionally, the weakening of the AC has been attributed to changes in local surface wind and the Indonesian Throughflow, which transports water from the Pacific Ocean to the Indian Ocean. However, our analysis suggests these changes cannot fully explain the AC changes in a warming climate. In this study, we show that remote processes in the North Atlantic could also contribute substantially to the AC weakening. In a warming climate, the Atlantic overturning circulation slows down and modifies the density structure of the Atlantic, which propagates into the Indian Ocean via wave processes and causes a weakening and shoaling of the AC. Our results highlight the importance of remote processes in future ocean circulation changes. Key Points: Climate models consistently project the Agulhas Current (AC) to weaken in the 21st centuryChanges in Indo‐Pacific wind and Atlantic overturning both contribute to the projected AC weakeningThe AC becomes shallower in a warming climate mainly due to the weakening of the Atlantic overturning [ABSTRACT FROM AUTHOR]