Asian Monsoon rainfall supports the livelihood of billions of people, yet the relative importance of different drivers remains an issue of great debate. Here, we present 30 million-year model-based reconstructions of Indian summer monsoon and South East Asian monsoon rainfall at millennial resolution. We show that precession is the dominant direct driver of orbital variability, although variability on obliquity timescales is driven through the ice sheets. Orographic development dominated the evolution of the South East Asian monsoon, but Indian summer monsoon evolution involved a complex mix of contributions from orography (39%), precession (25%), atmospheric CO2 (21%), ice-sheet state (5%) and ocean gateways (5%). Prior to 15 Ma, the Indian summer monsoon was broadly stable, albeit with substantial orbital variability. From 15 Ma to 5 Ma, strengthening was driven by a combination of orography and glaciation, while closure of the Panama gateway provided the prerequisite for the modern Indian summer monsoon state through a strengthened Atlantic meridional overturning circulation.