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Meta-learning is a branch of machine learning which trains neural network models to synthesize a wide variety of data in order to rapidly solve new problems. In process control, many systems have similar and well-understood dynamics, which suggests it is feasible to create a generalizable controller through meta-learning. In this work, we formulate a meta reinforcement learning (meta-RL) control strategy that can be used to tune proportional--integral controllers. Our meta-RL agent has a recurrent structure that accumulates "context" to learn a system's dynamics through a hidden state variable in closed-loop. This architecture enables the agent to automatically adapt to changes in the process dynamics. In tests reported here, the meta-RL agent was trained entirely offline on first order plus time delay systems, and produced excellent results on novel systems drawn from the same distribution of process dynamics used for training. A key design element is the ability to leverage model-based information offline during training in simulated environments while maintaining a model-free policy structure for interacting with novel processes where there is uncertainty regarding the true process dynamics. Meta-learning is a promising approach for constructing sample-efficient intelligent controllers.