Recent increases in vegetation cover, observed over much of the world, reflect increasing CO2 globally and warming in cold areas. However, the strength of the response to both CO2 and warming appears to be declining. Here we examine changes in vegetation cover on the Tibetan Plateau over the past 35 years. Although the climate trends are similar across the Plateau, drier regions have become greener by 0.31±0.14% yr−1 while wetter regions have become browner by 0.12±0.08% yr–1. This divergent response is predicted by a universal model of primary production accounting for optimal carbon allocation to leaves, subject to constraint by water availability. Rising CO2 stimulates production in both greening and browning areas; increased precipitation enhances growth in dry regions, but growth is reduced in wetter regions because warming increases below-ground allocation costs. The declining sensitivity of vegetation to climate change reflects a shift from water to energy limitation.