Organisms from diverse phylogenetic origins can thrive within the same ecological niches. They might be induced to evolve convergent adaptations in response to a similar landscape of selective pressures. Their genomes should bear the signature of this process. The study of unrelated virus lineages infecting the same host panels guarantees a clear identification of phyletically independent convergent adaptation. Here, we investigate the evolutionary history of genes in the accessory genome shared by unrelated insect large dsDNA viruses: the entomopoxviruses (EPVs, Poxviridae) and the baculoviruses (BVs). EPVs and BVs have overlapping ecological niches and have independently evolved similar infection processes. They are, in theory, subjected to the same selective pressures from their host's immune responses. Their accessory genomes might, therefore, bear analogous genomic signatures of convergent adaption and could point out key genomic mechanisms of adaptation hitherto undetected in viruses. We uncovered 32 homologous, yet independent acquisitions of genes originating from insect hosts, different eukaryotes, bacteria and viruses. We showed different evolutionary levels of gene acquisition convergence in these viruses, underlining a continuous evolutionary process. We found both recent and ancient gene acquisitions possibly involved to the adaptation to both specific and distantly related hosts. Multidirectional and multipartite gene exchange networks appear to constantly drive exogenous gene assimilations, bringing key adaptive innovations and shaping the life histories of large DNA viruses. This evolutionary process might lead to genome level adaptive convergence.