Solid organ transplantation disrupts virus-host relationships, potentially resulting in viral transfer from donor to recipient, reactivation of latent viruses, and new viral infections. Viral transfer, colonization, and reactivation are typically monitored using assays for specific viruses, leaving the behavior of full viral populations (the "virome") understudied. Here we sought to investigate the temporal behavior of viruses from donor lungs and transplant recipients comprehensively. We interrogated the bronchoalveolar lavage and blood viromes during the peritransplant period and 6-16 months posttransplant in 13 donor-recipient pairs using shotgun metagenomic sequencing. Anelloviridae, ubiquitous human commensal viruses, were the most abundant human viruses identified. Herpesviruses, parvoviruses, polyomaviruses, and bacteriophages were also detected. Anelloviridae populations were complex, with some donor organs and hosts harboring multiple contemporaneous lineages. We identified transfer of Anelloviridae lineages from donor organ to recipient serum in 4 of 7 cases that could be queried, and immigration of lineages from recipient serum into the allograft in 6 of 10 such cases. Thus, metagenomic analyses revealed that viral populations move between graft and host in both directions, showing that organ transplantation involves implantation of both the allograft and commensal viral communities.