Reliable and accurate streamflow simulation has a vital role in water resource development, mainly in agriculture, environment, domestic water supply, hydropower generation, flood control, and early warning systems. In this context, these days, deep learning algorithms have got enormous attention due to their high-performance simulation capacity. In this study, we compared multilayer perceptron (MLP), long short-term memory (LSTM), and gated recurrent unit (GRU) with the proposed new hybrid models, including CNN-LSTM and CNN-GRU. Hence, we can simulate one-step daily streamflow in different agroclimatic conditions, rolling time windows, and a range of variable input combinations. The analysis used daily multivariate and multisite time series data collected from Awash River Basin (Borkena watershed: Ethiopia) and Tiber River Basin (Upper Tiber River Basin: Italy) stations. The datasets were subjected to rigorous quality control processes. Consequently, it rolled to a different time lag to remove noise in the time series and further split into training and testing datasets using a ratio of 80 : 20, respectively. Finally, the results showed that integrating the GRU layer with the convolutional layer and using monthly rolled average daily input time series could substantially improve the simulation of streamflow time series.