Past sea-level changes in the Mediterranean Sea are highly non-uniform and can deviate significantly from both the global average sea-level rise and changes in the nearby Atlantic. Understanding the causes of this spatial non-uniformity is crucial to the success of coastal adaptation strategies. This, however, remains a challenge owing to the lack of long sea-level records in the Mediterranean. Previous studies have addressed this challenge by reconstructing past sea levels through objective analysis of sea-level observations. Such reconstructions have enabled significant progress towards quantifying sea-level changes, however, they have difficulty capturing long-term changes and provide little insight into the causes of the changes. Here, we combine data from tide gauges and altimetry with sea-level fingerprints of contemporary land-mass changes using spatial Bayesian methods to estimate the sources of sea-level changes in the Mediterranean Sea since 1960. We find that sea level in the Mediterranean rose slowly until 1990 (0.4±0.5 mm yr^-1), at which point it started accelerating significantly, driven by both sterodynamic changes and land-ice loss, reaching an average rate of 3.4±0.3 mm yr^-1 in the period 2000-2018. The rate of sea-level rise shows considerable spatial variation in the Mediterranean Sea, primarily reflecting changes in the large-scale circulation of the basin. Since 2000, sea level has been rising faster in the Adriatic, Aegean, and Levantine Seas than anywhere else in the Mediterranean Sea.