Geographically separated populations can convergently adapt to the same selection pressure. Convergent evolution at the level of a gene may arise via three distinct modes. The selected alleles can (1) have multiple independent mutational origins, (2) spread throughout subpopulations via gene flow, or (3) be shared due to shared ancestral standing variation. To understand the impact of convergent positive selection on neutral diversity at linked loci, we make use of the fact that hitchhiking can be modeled as an increase in the variance in neutral allele frequencies around a selected site within a population. We develop coalescent theory to show how shared hitchhiking events between subpopulations act to increase covariance in allele frequencies between subpopulations at loci near the selected site, and extend this theory under different models of migration and selection on the same standing variation. We incorporate this hitchhiking effect into a multivariate normal model of allele frequencies that also accounts for population structure. Based on this theory we present a composite likelihood-based approach that utilizes genomic data to identify loci involved in convergence, and distinguishes among alternate modes of convergent adaptation. We illustrate our method on genome-wide polymorphism data from four populations of killifish (Fundulus heteroclitus) that show very rapid convergent adaptation for tolerance to industrial pollutants. We identify a single locus at which both independent mutation events and migration play a role in adaptation across the species’ range.