Desertification in the Tibetan Plateau (TP) has drawn increasing attention in the recent decades. It has been postulated as a consequence of increasing climate aridity due to the observed warming. This study quantifies the aridity changes in the TP and attributes the changes to different climatic factors. Using the ratio of precipitation to potential evapotranspiration (P/PET) as an aridity index, we used observed meteorological records at 83 stations in the TP to calculate PET using the Penman–Monteith algorithm and the ratio. Spatial and temporal changes of P/PET in 1979–2011 were analyzed. Results show that stations located in the arid and semi-arid northwestern TP are becoming significantly wetter, and half of the stations in the semi-humid eastern TP are becoming drier, though not significantly, in the recent three decades. The aridity change patterns are significantly correlated with the change patterns of precipitation, sunshine duration and diurnal temperature range. Temporal correlations between the annual P/PET ratio and other meteorological variables confirm the significant correlation between aridity and the three variables, with precipitation being the dominant driver of P/PET changes at the interannual time scale. Annual PET are insignificantly but negatively correlated with P/PET in the cold season. In the warm season, however, the correlation between PET and P/PET is significant at the confidence level of 99.9% when the cryosphere near the surface melts. Significant correlation between annual wind speed and aridity occurs in limited locations and months. Consistency in the climatology pattern and linear trends in surface air temperature and precipitation calculated using station data, gridded data, and nearest grid-to-stations for the TP average and across sub-basins indicate the robustness of the trends despite the large spatial heterogeneity in the TP that challenge climate monitoring.