Some of the rainiest regions on Earth lie upstream of tropical mountains, where the interaction of prevailing winds with orography produces frequent precipitating convection. Yet, the response of tropical orographic precipitation to the large-scale wind and temperature variations induced by anthropogenic climate change remains largely unconstrained. Here, we quantify the sensitivity of tropical orographic precipitation to background cross-slope wind using theory, idealized simulations, and observations. We build on a recently developed theoretical framework that predicts enhanced seasonal-mean convective precipitation in response to cooling and moistening of the lower free-troposphere by stationary orographic gravity waves. Using this framework and convection-permitting simulations, we show that higher cross-slope wind speeds deepen the penetration of the cool and moist gravity wave perturbation upstream of orography, resulting in a mean rainfall increase of 20–30 % per m s−1 increase in cross-slope wind speed. Additionally, we show that orographic precipitation in five tropical regions exhibits a similar dependence on changes in cross-slope wind at both seasonal and daily timescales. Given next-century changes in large-scale winds around tropical orography projected by global climate models, this strong scaling rate implies wind-induced changes in some of Earth’s rainiest regions that are comparable with any produced directly by increases in global mean temperature and humidity.