Microgrids incorporated with distributed generation (DG) units and energy storage (ES) devices are expected to play more and more important roles in the future power systems. Yet, achieving efficient distributed economic dispatch in microgrids is a challenging issue due to the randomness and nonlinear characteristics of DG units and loads. This paper proposes a cooperative reinforcement learning algorithm for distributed economic dispatch in microgrids. Utilizing the learning algorithm can avoid the difficulty of stochastic modeling and high computational complexity. In the cooperative reinforcement learning algorithm, the function approximation is leveraged to deal with the large and continuous state spaces. And a diffusion strategy is incorporated to coordinate the actions of DG units and ES devices. Based on the proposed algorithm, each node in microgrids only needs to communicate with its local neighbors, without relying on any centralized controllers. Algorithm convergence is analyzed, and simulations based on real-world meteorological and load data are conducted to validate the performance of the proposed algorithm.