The strong present-day Asian monsoons are thought to have originated between 25 and 22 million years (Myr) ago, driven by Tibetan-Himalayan uplift. However, the existence of older Asian monsoons and their response to enhanced greenhouse conditions such as those in the Eocene period (55-34 Myr ago) are unknown because of the paucity of well-dated records. Here we show late Eocene climate records revealing marked monsoon-like patterns in rainfall and wind south and north of the Tibetan-Himalayan orogen. This is indicated by low oxygen isotope values with strong seasonality in gastropod shells and mammal teeth from Myanmar, and by aeolian dust deposition in northwest China. Our climate simulations support modern-like Eocene monsoonal rainfall and show that a reinforced hydrological cycle responding to enhanced greenhouse conditions counterbalanced the negative effect of lower Tibetan relief on precipitation. These strong monsoons later weakened with the global shift to icehouse conditions 34 Myr ago.