Barystatic sea level rise (SLR) caused by the addition of freshwater to the ocean from melting ice can in principle be recorded by a reduction in seawater salinity, but detection of this signal has been hindered by sparse data coverage and the small trends compared to natural variability. Here, we develop an autoregressive machine learning method to estimate salinity changes in the global ocean from 2001 to 2019 that reduces uncertainties in ocean freshening trends by a factor of four compared to previous estimates. We find that the ocean mass rose by 13,000 ± 3,000 Gt from 2001 to 2019, implying a barystatic SLR of 2.0 ± 0.5 mm/yr. Combined with SLR of 1.3 ± 0.1 mm/yr due to ocean thermal expansion, these results suggest that global mean sea level rose by 3.4 ± 0.6 mm/yr from 2001 to 2019. These results provide an important validation of remote‐sensing measurements of ocean mass changes, global SLR, and global ice budgets. Plain Language Summary Global sea level rise (SLR) is caused by heating of the ocean, and by the input of freshwater from the melting of glaciers and ice caps. Global freshwater input to the oceans from melting ice during the 21st century has primarily been tracked by satellites that measure changes in the mass of the ocean. Here, we show that trends in global SLR can also be accurately tracked by global observations of ocean salinity changes, as freshwater runoff from melting ice enters the ocean and dilutes ocean salinity. These results show that ocean salinity measurements are critical for monitoring global sea level changes, particularly as polar warming intensifies and the melting of ice sheets accelerates. Key Points A new full‐depth ocean salinity product yields robust global freshening trend of (35 ± 10) × 10−6 yr−1 from 2001 to 2019 Combined with estimates of sea ice loss, this freshening implies that ocean mass rose by 13,000 ± 3,000 Gt from 2001 to 2019 Sea level rise derived from ocean temperature and salinity measurements is 3.4 ± 0.6 mm/yr, confirming the satellite altimetry trend