The tropospheric delay is a major error source for space geodetic techniques, and the performance of its modeling is significantly limited due to the high spatiotemporal variability of the moisture in the lower atmosphere. In this study, global modeling of the tropospheric zenith wet delay (ZWD) was realized based on surface meteorological data obtained from radiosondes and Global Positioning System (GPS) radio occultation (RO) measurements through the random forest (RF) and backpropagation neural network (BPNN) regression analysis. The modeling performance was further validated based on two kinds of global atmospheric profiles for the year 2020. Our results show that the ZWD modeling accuracy gained by two machine learning regression approaches is significantly improved by taking into account surface meteorological parameters, especially the surface water vapor pressure when compared to the Global Pressure and Temperature 3 (GPT3) model. When surface meteorological data are available, the RF-B model yields ZWD estimations with an overall agreement of 3.1 cm in comparison with the sounding profiles and 2.4 cm in contrast to the GPS RO atmospheric profiles. The RF-B is superior to other models based on surface meteorological parameters for ZWD calculation, e.g., the accuracy improves by 21.8–23.8% against the approach by Saastamoinen and 7–12.2% against the formula by Askne and Nordius.