The combination of data acquired by Landsat-8 and Sentinel-2 earth observation missions produces dense time series (TSs) of multispectral images that are essential for monitoring the dynamics of land-cover and land-use classes across the earth's surface with high temporal resolution. However, the optical sensors of the two missions have different spectral and spatial properties, thus they require a harmonization processing step before they can be exploited in remote sensing applications. In this work, we propose a workflow-based on a deep learning approach to harmonize these two products developed and deployed on an high-performance computing environment. In particular, we use a multispectral generative adversarial network with a U-Net generator and a PatchGan discriminator to integrate existing Landsat-8 TSs with data sensed by the Sentinel-2 mission. We show a qualitative and quantitative comparison with an existing physical method [National Aeronautics and Space Administration (NASA) Harmonized Landsat and Sentinel (HLS)] and analyze original and generated data in different experimental setups with the support of spectral distortion metrics. To demonstrate the effectiveness of the proposed approach, a crop type mapping task is addressed using the harmonized dense TS of images, which achieved an overall accuracy of 87.83% compared to 81.66% of the state-of-the-art method.