Climate change is asymmetrically altering environmental conditions in space, from local to global scales, creating novel heterogeneity. Here, we argue that this novel heterogeneity will drive mobile generalist consumer species to rapidly respond through their behaviour in ways that broadly and predictably reorganize - or rewire - food webs. We use existing theory and data from diverse ecosystems to show that the rapid behavioural responses of generalists to climate change rewire food webs in two distinct and critical ways. First, mobile generalist species are redistributing into systems where they were previously absent and foraging on new prey, resulting in topological rewiring - a change in the patterning of food webs due to the addition or loss of connections. Second, mobile generalist species, which navigate between habitats and ecosystems to forage, will shift their relative use of differentially altered habitats and ecosystems, causing interaction strength rewiring - changes that reroute energy and carbon flows through existing food web connections and alter the food web's interaction strengths. We then show that many species with shared traits can exhibit unified aggregate behavioural responses to climate change, which may allow us to understand the rewiring of whole food webs. We end by arguing that generalists' responses present a powerful and underutilized approach to understanding and predicting the consequences of climate change and may serve as much-needed early warning signals for monitoring the looming impacts of global climate change on entire ecosystems.