Path integration is a widespread navigational strategy in which directional changes and distance covered are continuously integrated on an outward journey, enabling a straight-line return to home. Bees use vision for this task – a celestial-cue based visual compass, and an optic-flow based visual odometer – but the underlying neural integration mechanisms are unknown. Using intracellular electrophysiology, we show that polarized-light based compass-neurons and optic flow-based speed-encoding neurons converge in the central complex of the bee brain, and through block-face electron microscopy we identify potential integrator cells. Based on plausible output targets for these cells, we propose a complete circuit for path integration and steering in the central complex, with anatomically-identified neurons suggested for each processing step. The resulting model-circuit is thus fully constrained biologically and provides a functional interpretation for many previously unexplained architectural features of the central complex. Moreover, we show that the receptive fields of the newly discovered speed neurons can support path integration for the holonomic motion (i.e. a ground velocity that is not precisely aligned with body orientation) typical of bee-flight, a feature not captured in any previously proposed model of path integration. In a broader context, the model-circuit presented provides a general mechanism for producing steering signals by comparing current and desired headings – suggesting a more basic function for central-complex connectivity from which path integration may have evolved.