A new inversion algorithm has been developed for the retrieval of tropospheric wet path delay from microwave radiometer measurements. The algorithm is based on the principle of maximum probability and uses Bayes' theorem to determine the most probable state vector (comprised of discrete height profiles of temperature and water vapor density) for a given set of measurements. The solution probabilities depend both on conformity to apriori statistics and a minimization of residuals between measured observables and observables computed from candidate state vectors. The new algorithm has been compared with standard statistical inversion techniques using simulations based on radiosonde, lidar, and acoustic sounding measurements of atmospheric temperature and water vapor profiles. For clear conditions the results indicate that the nonlinear algorithm produces a factor of 3–5 improvement in path delay retrieval performance, relative to a nonstratified statistical algorithm, when the observational system includes both a water vapor radiometer and a microwave temperature profiler and measurement errors are minimized. The new algorithm is shown to be most useful when applied to radiometric measurements of path delay fluctuations over minute to multihour timescales. Recommended applications include tropospheric calibration systems for radio science experiments such as very long baseline interferometry astrometry and the planned Cassini gravitational wave experiment.