The variations of global mean sea level are an important indicator of global climate change, and their measurement can provide important information for determining the socioeconomic impact of sea level change on coastal land use. The analysis of historical tide gauge records generally indicates that sea level has risen at a rate of about 2 mm/yr during the last 100 years; however, this estimate is somewhat uncertain due to the effects of regional crustal motion, lack of uniform temporal coverage, and the limited spatial sampling of tide gauges. The prospect of measuring variations in global mean sea level has been assessed using approximately 2.5 years of satellite altimeter data from the TOPEX/POSEIDON (T/P) mission, where synoptic mapping of the geocentric height of the ocean surface is routinely achieved with a point‐to‐point accuracy of better than 5 cm. The global mean sea level variations measured by T/P every 10 days have an rms of 6 mm (4 mm after detrending), some of which is shown to be correlated with sea surface temperature variations. The rate of change of global mean sea level derived from 2.5 years of data is +5.8 mm/yr with a scatter of 0.7 mm/yr. Currently, it is impossible to accurately estimate the error in the measured rate of sea level rise, since little is known about the long‐term behavior of the measurement errors at the millimeter level. In addition, there is evidence from the sea surface temperature record that the measured rate of sea level rise is associated with a relatively short‐term (interannual) variation unrelated to the long‐term signal expected from global warming. Nevertheless, these results suggest that T/P is achieving the necessary repeatability to measure global sea level variations caused by climate change, and a longer time series will significantly improve the sea level rise estimate by averaging measurement error and real sea level variations. A longer time series will also reduce the errors in estimates of the altimeter calibration, providing an important constraint on any long‐term instrument drift. Future research will focus on establishing a realistic error budget for these measurements of global mean sea level, so that they can be put in the proper context with other observations of global climate change.