Marine voyage optimization determines the optimal route and speed to ensure timely arrival. The problem becomes particularly complex when incorporating a dynamic environment, such as future expected weather conditions along the route and unexpected disruptions. This study explores two model-free Deep Reinforcement Learning (DRL) algorithms: (i) a Double Deep Q Network (DDQN) and (ii) a Deep Deterministic Policy Gradient (DDPG). These algorithms are computationally costly, so we split optimization into an offline phase (costly pre-training for a route) and an online phase where the algorithms are fine-tuned as updated weather data become available. Fine tuning is quick enough for en-route adjustments and for updating the offline planning for different dates where the weather might be very different. The models are compared to classical and heuristic methods: the DDPG achieved a 4% lower fuel consumption than the DDQN and was only outperformed by Tabu Search by 1%. Both DRL models demonstrate high adaptability to dynamic weather updates, achieving up to 12% improvement in fuel consumption compared to the distance-based baseline model. Additionally, they are non-graph-based and self-learning, making them more straightforward to extend and integrate into future digital twin-driven autonomous solutions, compared to traditional approaches.