We present a Bayesian method to map contemporary rates of relative sea level change using a joint inversion of vertical trends from tide gauges, GPS time series, and satellite radar altimetry measurements. Tide gauge measurements constrain rates of relative sea level change on decadal to secular time scales at a few hundred sites sparsely distributed along coastlines. Predicting the rates of relative sea level change from historical tide gauge measurements is difficult due to the paucity and uneven distribution of sites with high quality records. Since the late twentieth century, deployments of GPS stations have enabled accurate determination of the rates of vertical land motion. A series of satellite radar altimetry missions provide continuous and global monitoring of geocentric sea level changes since the launch of TOPEX/Poseidon in 1992. By combining these three observations types into a single Bayesian inversion, we construct continuous maps of rates of relative sea level change, geocentric sea level change, and vertical land motion assuming linear trends, with robust estimates of uncertainties at regional scales. Cross-validation tests show that reliable predictions of relative sea level changes are still provided where only GPS and satellite altimetry data are used, suggesting this method is viable for studying potential sea level risk for communities where historical tide gauge data are not available. Our results provide spatially and temporally consistent estimates of the various contributions to relative sea level changes.