Observed evaporative demand has decreased worldwide during the past several decades. This trend is also noted on the Tibetan Plateau, a region that is particularly sensitive to climate change. However, patterns and trends of evapotranspiration and their relationship to drought stress on the Tibetan Plateau are complex and poorly understood. Here, we analyze spatiotemporal changes in evapotranspiration and effective moisture (defined as the ratio of actual evapotranspiration (ETa) to reference crop evapotranspiration (ETo)) based on the modified Lund-Potsdam-Jena Dynamic Global Vegetation Model (LPJ). Climate data from 80 meteorological stations on the Tibetan Plateau were compiled for the period 1981–2010 and future climate projections were generated by a regional climate model through the 21st century. The results show regional trends towards decreasing ETo and statistically significant increases in ETa (p < 0.05) and effective moisture during the period 1981–2010 (p < 0.001). A transition from significant negative to positive ETo occurred in 1997. Additionally, a pronounced increase in effective moisture occurred during the period 1981–1997 because of significant decreased ETo before 1997. In the future, regional ETo and ETa are projected to increase, thus reducing drought stress, because of generally increased effective moisture. Future regional differences are most pronounced in terms of effective moisture, which shows notable increases in the northwestern plateau and decreases in the southeastern plateau. Moreover, the reduced magnitude of effective moisture is likely to intensify in the long term, due mainly to increased evaporative demand.