Migrating eastern North American monarch butterflies use a time-compensated sun compass to adjust their flight to the southwest direction. Although the antennal genetic circadian clock and the azimuth of the sun are instrumental for proper function of the compass, it is unclear how these signals are represented on a neuronal level and how they are integrated to produce flight control. To address these questions, we constructed a receptive field model of the compound eye that encodes the solar azimuth. We then derived a neural circuit model that integrates azimuthal and circadian signals to correct flight direction. The model demonstrates an integration mechanism, which produces robust trajectories reaching the southwest regardless of the time of day and includes a configuration for remigration. Comparison of model simulations with flight trajectories of butterflies in a flight simulator shows analogous behaviors and affirms the prediction that midday is the optimal time for migratory flight.