Cloud cover plays a critical role in weather prediction and impacts several sectors, including agriculture, solar power generation, and aviation. Despite advancements in numerical weather prediction (NWP) models, forecasting total cloud cover remains challenging due to the small-scale nature of cloud formation processes. In this study, we introduce CloudCast, a convolutional neural network (CNN) based on the U-Net architecture, designed to predict total cloud cover (TCC) up to five hours ahead. Trained on five years of satellite data, CloudCast significantly outperforms traditional NWP models and optical flow methods. Compared to a reference NWP model, CloudCast achieves a 24% lower mean absolute error and reduces multi-category prediction errors by 46%. The model demonstrates strong performance, particularly in capturing the large-scale structure of cloud cover in the first few forecast hours, though later predictions are subject to blurring and underestimation of cloud formation. An ablation study identified the optimal input features and loss functions, with MAE-based models performing the best. CloudCast has been integrated into the Finnish Meteorological Institute's operational nowcasting system, where it improves cloud cover forecasts used by public and private sector clients. While CloudCast is limited by a relatively short skillful lead time of about three hours, future work aims to extend this through more complex network architectures and higher-resolution data. CloudCast code is available at https://github.com/fmidev/cloudcast.