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Roundabouts promise potential safety and efficiency benefits in the homogenous environment of conventional vehicles. However, their performance can deteriorate if high and/or imbalanced traffic exists. The advent of connected and automated vehicles (CAVs) has provided great opportunities to make transportation infrastructures more efficient. The purpose of this study is to develop a model to optimally control CAVs at roundabouts under a fully CAV environment. A two‐stage optimization model is proposed to optimize vehicle trajectories. At the first stage, a mixed‐integer linear programming model is formulated that optimizes vehicle arrival time at the roundabout. Then the optimal arrival time is fed to the second stage model to optimize vehicle trajectories, which is a non‐linear programming model. CAVs are guaranteed to pass the roundabout safely without stops. Simulation tests are carried out with different …