Oil spills pose a major threat of the oceanic and coastal environments, hence, an automatic detection and a continuous monitoring system comprises an appealing option for minimizing the response time of any relevant operation. Numerous efforts have been conducted towards such solutions by exploiting a variety of sensing systems. Previous studies, including neural networks, have shown that the use of satellite Synthetic Aperture Radar (SAR) can effectively identify oil spills over sea surfaces in any environmental conditions and operational time. Moreover, in recent years, deep Convolutional Neural Networks (CNN) have presented some remarkable abilities to surpass previous state-of-the-Art performances in a great diversity of fields including identification tasks. This paper describes the development of an approach that combines the merits of a deep CNN with SAR imagery in order to provide a fully automated oil spill detection system. The deployed CNN was trained using multiple SAR images acquired from the sentinel-1 satellite provided by ESA and based on EMSA records for maritime pollution events. Experiments on such challenging benchmark datasets demonstrate that the algorithm can accurately identify oil spills leading to an effective detection solution.