In recent years, Machine Learning (ML) algorithms have become widespread in all the fields of Remote Sensing (RS) and Earth Observation (EO). This has allowed the rapid development of new procedures to solve problems affecting these sectors. In this context, this work aims at presenting a novel method for filtering speckle noise from Sentinel-1 Ground Range Detected (GRD) data by applying Deep Learning (DL) algorithms, based on Convolutional Neural Networks (CNNs). The paper provides an easy yet very effective approach to extract the large amount of training data needed for DL approaches in this challenging case. The experimental results on simulated speckled images and an actual SAR dataset show a clear improvement with respect to the state of the art in terms of Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index (SSIM), Equivalent Number of Looks (ENL), proving the effectiveness of the proposed architecture.