Food webs are highly complex ecological networks, dynamic in both space and time. Metacommunity models are now at the core of unified theories of biodiversity, but to date they have not addressed food web complexity. Here we show that metacommunity theory can explain the emergence of species-rich food webs with complex network topologies. Our analysis shows that network branching in the food web is maximized at intermediate colonization rates and limited dispersal scales, which also leads to concomitant peaks in species diversity. Increased food web complexity and species diversity are made possible by the structural role played by network branches that are supported by omnivore and generalist feeding links. Thus, in contrast to traditional food web theory, which emphasizes the destabilizing effect of omnivory feeding in closed systems, metacommunity theory predicts that these feeding links, which are commonly observed in empirical food webs, play a critical structural role as food webs assemble in space. As this mechanism functions at the metacommunity level, evidence for its operation in nature will be obtained through multiscale surveys of food web structure. Finally, we apply our theory to reveal the effects of habitat destruction on network complexity and metacommunity diversity.