The hydroclimate of the Tibetan Plateau (TP) and Central Asia (CA) plays a crucial role in sustaining surface water reservoirs and thus water resources in the respective regions. In this study, we investigate the changes in Asian hydroclimate and its driving forces during specific time intervals in the last 3 Ma. We conduct high‐resolution (∼0.75° per grid cell) general circulation model ECHAM‐5 experiments with boundary conditions for the mid‐Pliocene (∼3 Ma), the Last Glacial Maximum (LGM; ∼21 ka), the mid‐Holocene (∼6 ka), and the pre‐industrial. Results suggest that seasonally relatively high precipitation rates (>1 mm day−1) were longer in the mid‐Pliocene and shorter in the LGM, relative to the pre‐industrial. We calculate different monsoon indices to detect changes in the intensity, strength and duration of the East Asian summer monsoon (EASM), South Asian summer monsoon (SASM), and the Indian summer monsoon (ISM), and construct climatologies of mid‐latitude high‐level westerly jet (WJ) stream occurrences based on the ECHAM5 wind fields. Our results suggest that in warm periods (e.g., mid‐Pliocene or interglacial), the WJ migrates northward earlier in the year (April) and reaches higher latitudes than in the pre‐industrial, resulting in a wetter TP and CA. During cooler periods (e.g., LGM or glacial), the WJ migrates northward later in the year (June) and remains over lower latitudes, resulting in a drier TP and CA. Increased/decreased local precipitation in TP and CA for the mid‐Pliocene/LGM experiments correlates strongly with (a) intensity, strength and duration of the EASM, SASM, and the ISM and (b) WJ latitudinal position.