Instrumental and proxy records indicate remarkable global climate variability over the last millennium, influenced by solar irradiance, Earth's orbital parameters, volcanic eruptions and human activities. Numerical model simulations and proxy data suggest an enhanced Asian summer monsoon during the Medieval Warm Period (MWP) compared to the Little Ice Age (LIA). Using multiple climate model simulations, we show that anomalous seasonal insolation over the Northern Hemisphere due to a long cycle of orbital parameters results in a modulation of the Asian summer monsoon transition between the MWP and LIA. Ten climate model simulations prescribing historical radiative forcing that includes orbital parameters consistently reproduce an enhanced MWP Asian monsoon in late summer and a weakened monsoon in early summer. Weakened, then enhanced Northern Hemisphere insolation before and after June leads to a seasonally asymmetric temperature response over the Eurasian continent, resulting in a seasonal reversal of the signs of MWP-LIA anomalies in land-sea thermal contrast, atmospheric circulation, and rainfall from early to late summer. This seasonal asymmetry in monsoon response is consistently found among the different climate models and is reproduced by an idealized model simulation forced solely by orbital parameters. The results of this study indicate that slow variation in the Earth's orbital parameters contributes to centennial variability in the Asian monsoon transition.