The diverse collections of microorganisms associated with humans and other animals, collectively referred to as their "microbiome," are critical for host health, but the mechanisms that govern their assembly are poorly understood. This has made it difficult to identify consistent host factors that explain variation in microbiomes across hosts, despite large-scale sampling efforts. While ecological theory predicts that the movement, or dispersal, of individuals can have profound and predictable consequences on community assembly, its role in the assembly of animal-associated microbiomes remains underexplored. Here, we show that dispersal of microorganisms among hosts can contribute substantially to microbiome variation, and is able to overwhelm the effects of individual host factors, in an experimental test of ecological theory. We manipulated dispersal among wild-type and immune-deficient knockout zebrafish and observed that interhost dispersal had a large effect on the diversity and composition of intestinal microbiomes. Interhost dispersal was strong enough to overwhelm the effects of host factors, largely eliminating differences between wild-type and immune-deficient hosts, regardless of whether dispersal occurred within or between genotypes, suggesting dispersal can independently alter the ecology of microbiomes. Our observations are consistent with a predictive model that assumes metacommunity dynamics and are likely mediated by dispersal-related microbial traits. These results illustrate the importance of microbial dispersal to animal microbiomes and motivate its integration into the study of host-microbe systems.