Migrating monarch butterflies (Danaus plexippus) use a time-compensated sun compass to navigate from eastern North America to their overwintering grounds in central Mexico. We have described the neuronal layout of those aspects of the butterfly brain central complex likely to establish part of the internal sun compass. Neuronal responses to eye-mediated skylight cues are integrated to create a consistent representation of those cues in the sun compass throughout the day. The sun compass timing elements reside in light-entrained circadian clocks in the antennae. Our work shows that clock outputs from each antenna are processed and integrated together in the monarch time-compensated sun compass circuit. We also generated a standardized average-shape representation of the central complex and related brain regions and used this tool to identify central complex input pathways, intrinsic neurons, and output pathways. We discovered that coldness triggers the northward flight direction in spring remigrants and that remigrants also use an antenna-dependent time-compensated sun compass to navigate. We have shown that migrant monarchs possess a light-dependent inclination magnetic compass, setting the stage for understanding the molecular mechanism of magnetoreception.