Most coupled model simulations substantially overestimate tropical tropospheric warming trends over the satellite era, undermining the reliability of model-projected future climate change. Here we show that the model-observation discrepancy over the satellite era has arisen in large part from multi-decadal climate variability and residual biases in the satellite record. Analyses indicate that although the discrepancy is closely linked to multi-decadal variability in the tropical Pacific sea surface temperatures, the overestimation remains over the satellite era in model simulations forced by observed time-varying sea surface temperatures with a La Niña-like pattern. Regarding moist thermodynamic processes governing tropical tropospheric warming, however, we find a broad model-observation consistency over a post-war period, suggesting that residual biases in the satellite record may contribute to model-observation discrepancy. These results underscore the importance of sustaining an accurate long-term observing system as well as constraining the model representation of tropical Pacific sea surface temperature change and variability.