Accurate monthly runoff prediction is significant to extreme flood control and water resources management. However, traditional statistical models without multi-variable input may fail to capture runoff changes effectively due to the dual effect of climate change and human activities. Here, we used five multi-input machine learning (ML) models to predict monthly runoff, where multiple global circulation indexes and surface meteorological indexes were selected as explanatory variables by the stepwise regression or copula entropy methods. Moreover, four univariate models were adopted as benchmarks. The multi-input ML models were tested at two typical hydrological stations (i.e., Gaochang and Cuntan) in the Upper Yangtze River. The results indicate that the LSTM_Copula (long short-term memory model combined with copula entropy method) model outperformed other models in both hydrological stations, while the GRU_Step (gate recurrent unit model combined with stepwise regression method) model and the RF_Copula (random forest model combined with copula entropy method) model also showed satisfactory performances. In addition, the ML models with multi-variable input provided better predictability compared with four univariate statistical models, and the MAPE (mean absolute percentage error), RMSE (root mean square error), NSE (Nash–Sutcliffe efficiency coefficient), and R (Pearson’s correlation coefficient) values were improved by 5.10, 4.16, 5.34, and 0.43% for the Gaochang Station, and 10.84, 17.28, 13.68, and 3.55% for the Cuntan Station, suggesting the proposed ML approaches are practically applicable to monthly runoff forecasting in large rivers.