We empirically tested the long-standing hypothesis of codivergence of New World arenaviruses (NWA) with their hosts. We constructed phylogenies for NWA and all known hosts and used them in reconciliation analyses. We also constructed a phylogenetic tree of all Sigmodontinae and Neotominae rodents and tested whether viral–host associations were phylogenetically clustered. We determined host geographical overlap to determine to what extent opportunity to switch hosts was limited by host relatedness or physical proximity. With the exception of viruses from North America, no phylogenetically codivergent pattern between NWA and their hosts was found. We found that different virus clades were clustered differently and that Clade B with members pathogenic to humans was randomly distributed across the rodent phylogeny. Furthermore, viral relatedness within Clade B was significantly explained by the geographic overlap of their hosts’ ranges rather than host relatedness, indicating that they are capable of host switching opportunistically. This has important bearings on their potential to become panzootic. Together, these analyses suggest that NWA have not codiverged with their hosts and instead have evolved predominantly via host switching.