The multi-constellation Global Navigation Satellite Systems (GNSS) offers promising potential for the retrieval of real-time (RT) atmospheric parameters to support time-critical meteorological applications, such as nowcasting or regional short-term forecasts. In this study, we processed GNSS data from the globally distributed Multi-GNSS Experiment (MGEX) network of about 30 ground stations by using the precise point positioning (PPP) technique for retrieving RT multi-GNSS tropospheric delays. RT satellite orbit and clock product streams from the International GNSS Service (IGS) were used. Meanwhile, we assessed the quality of clock and orbit products provided by different IGS RT services, called CLK01, CLK81, CLK92, GFZC2, and GFZD2, respectively. Using the RT orbit and clock products, the performances of the RT zenith total delays (ZTD) retrieved from single-system as well as from multi-GNSS combined observations were evaluated by comparing with the U.S. Naval Observatory (USNO) final troposphere products. With the addition of multi-GNSS observations, RT ZTD estimates with higher accuracy and enhanced reliability compared to the single-system solution can be obtained. Compared with the Global Positioning System (GPS)-only solution, the improvements in the initialization time of ZTD estimates are about 5.8% and 8.1% with the dual-system and the four-system combinations, respectively. The RT ZTD estimates retrieved with the GFZC2 products outperform those derived from the other IGS-RT products. In the GFZC2 solution, the accuracy of about 5.05 mm for the RT estimated ZTD can be achieved with fixing station coordinates. The results also confirm that the accuracy improvement (about 22.2%) can be achieved for the real-time estimated ZTDs by using multi-GNSS observables, compared to the GPS-only solution. In the multi-GNSS solution, the accuracy of real-time retrieved ZTDs can be improved by a factor of up to 2.7 in the fixing coordinate mode, compared with that in the kinematic mode.