Sensory processing in the neocortex requires both feedforward and feedback information flow between cortical areas1. In feedback processing, higher-level representations provide contextual information to lower levels, and facilitate perceptual functions such as contour integration and figure–ground segmentation2,3. However, we have limited understanding of the circuit and cellular mechanisms that mediate feedback influence. Here we use long-range all-optical connectivity mapping in mice to show that feedback influence from the lateromedial higher visual area (LM) to the primary visual cortex (V1) is spatially organized. When the source and target of feedback represent the same area of visual space, feedback is relatively suppressive. By contrast, when the source is offset from the target in visual space, feedback is relatively facilitating. Two-photon calcium imaging data show that this facilitating feedback is nonlinearly integrated in the apical tuft dendrites of V1 pyramidal neurons: retinotopically offset (surround) visual stimuli drive local dendritic calcium signals indicative of regenerative events, and two-photon optogenetic activation of LM neurons projecting to identified feedback-recipient spines in V1 can drive similar branch-specific local calcium signals. Our results show how neocortical feedback connectivity and nonlinear dendritic integration can together form a substrate to support both predictive and cooperative contextual interactions.