Adaptive Operator Selection (AOS) is an approach that controls discrete parameters of an Evolutionary Algorithm (EA) during the run. In this paper, we propose an AOS method based on Double Deep Q-Learning (DDQN), a Deep Reinforcement Learning method, to control the mutation strategies of Differential Evolution (DE). The application of DDQN to DE requires two phases. First, a neural network is trained offline by collecting data about the DE state and the benefit (reward) of applying each mutation strategy during multiple runs of DE tackling benchmark functions. We define the DE state as the combination of 99 different features and we analyze three alternative reward functions. Second, when DDQN is applied as a parameter controller within DE to a different test set of benchmark functions, DDQN uses the trained neural network to predict which mutation strategy should be applied to each parent at each generation according to the DE state. Benchmark functions for training and testing are taken from the CEC2005 benchmark with dimensions 10 and 30. We compare the results of the proposed DE-DDQN algorithm to several baseline DE algorithms using no online selection, random selection and other AOS methods, and also to the two winners of the CEC2005 competition. The results show that DE-DDQN outperforms the non-adaptive methods for all functions in the test set; while its results are comparable with the last two algorithms.