When larval zebrafish experience whole-field visual motion, as in the random-dot task, they swim in the direction of motion - an innate behavior enabling animals to maintain position in moving water. This behavior is well-explained by the same drift-diffusion algorithm that captures human and primate behavior in analogous random-dot paradigms. We previously proposed a hypothetical circuit model that implements this algorithm via a recurrent integrator circuit in the zebrafish hindbrain that accumulates noisy visual evidence and excites downstream motor circuits after overcoming competitive inhibition from surrounding neurons. To test this model anatomically, we first photoactivated single neurons of interest identified with two-photon functional imaging and reconstructed their 3D morphologies at light microscopic resolution. Critically, different functional cell classes also constituted different morphotypes, e.g., cells with integration dynamics fell into an ipsilaterally and a contralaterally projecting morphotype, which were anatomically distinct from other functional cell classes. In parallel, we generated an anatomical library of hindbrain neurons reconstructed at synaptic resolution in an existing whole-brain electron microscopy (EM) volume of a different animal. In this EM library, we found six neurons that matched the functionally identified ipsilaterally projecting integrator morphotype and we reconstructed their monosynaptic and disynaptic postsynaptic partners. Consistent with our circuit model, integrator neurons were embedded in a recurrent network and projected to the motor nuclei of the reticulospinal system. Moreover, we also found an unpredicted circuit motif, consisting of integrator neurons that specifically targeted the raphe, which may constitute an anatomical pathway for gain adaption in the optomotor response.