Human gut microbiome composition is shaped by multiple factors but the relative contribution of host genetics remains elusive. Here we examine genotype and microbiome data from 1,046 healthy individuals with several distinct ancestral origins who share a relatively common environment, and demonstrate that the gut microbiome is not significantly associated with genetic ancestry, and that host genetics have a minor role in determining microbiome composition. We show that, by contrast, there are significant similarities in the compositions of the microbiomes of genetically unrelated individuals who share a household, and that over 20% of the inter-person microbiome variability is associated with factors related to diet, drugs and anthropometric measurements. We further demonstrate that microbiome data significantly improve the prediction accuracy for many human traits, such as glucose and obesity measures, compared to models that use only host genetic and environmental data. These results suggest that microbiome alterations aimed at improving clinical outcomes may be carried out across diverse genetic backgrounds. Statistical analyses of a metagenomics-sequenced human cohort identify a relatively minor role for genetics in determining microbiome composition and show that several human phenotypes are as strongly associated with the gut microbiome as with host genetics. The composition of the human gut microbiome is determined by many factors. Eran Segal and colleagues performed an extensive statistical analysis of the largest metagenomics-sequenced human cohort so far to determine the contribution of host genotype to microbiome composition. Host genetics has only a minor influence on microbiome variability, which is more strongly associated with environmental factors such as diet. The authors propose a 'microbiome-association index' that describes the association of the microbiome with host phenotype. Combining this measurement with host genetic and environmental data improves the accuracy of predictions about several human metabolic traits, such as glucose and obesity traits.