Real-time reconstruction of ocean surface currents is a challenge due to the complex, non-linear dynamics of the ocean, the small number of in situ measurements, and the spatio-temporal heterogeneity of satellite altimetry observations. To address this challenge, we introduce HIRES-CURRENTS-Net, an operational real-time convolutional neural network (CNN) model for daily ocean current reconstruction. This study focuses on the Mediterranean Sea, a region where operational models have great difficulty predicting surface currents. Notably, our model showcases higher accuracy compared to commonly used alternative methods. HIRES-CURRENTS-Net integrates high-resolution measurements from the infrared or visible spectrum—high resolution Sea Surface Temperature (SST) or chlorophyll (CHL) images—in addition to the low-resolution Sea Surface Height (SSH) maps derived from satellite altimeters. In the first stage, we apply a transfer learning method which uses a high-resolution numerical model to pre-train our CNN model on simulated SSH and SST data with synthetic clouds. The observation of System Simulation Experiments (OSSEs) offers us a sufficient training dataset with reference surface currents at very high resolution, and a model trained on this data can then be applied to real data. In the second stage, to enhance the real-time operational performance of our model over previous methods, we fine-tune the CNN model on real satellite data using a novel pseudo-labeling strategy. We validate HIRES-CURRENTS-Net on real data from drifters and demonstrate that our data-driven approach proves effective for real-time sea surface current reconstruction with potential operational applications such as ship routing.