Phosphodiesterases (PDEs) encoded by viruses are putatively acquired by horizontal transfer of cellular PDE ancestor genes. Viral PDEs inhibit the OAS-RNase L antiviral pathway, a key effector component of the innate immune response. Although the function of these proteins is well-characterized, the origins of these gene acquisitions is less clear. Phylogenetic analysis revealed at least five independent PDE acquisition events by ancestral viruses. We found evidence that PDE-encoding genes were horizontally transferred between coronavirus genera. Three clades of viruses within Nidovirales: merbecoviruses (MERS-CoV), embecoviruses (OC43), and toroviruses encode independently acquired PDEs, and a clade of rodent alphacoronaviruses acquired an embecovirus PDE via recent horizontal transfer. Among rotaviruses, the PDE of Rotavirus A was acquired independently from Rotavirus B and G PDEs, which share a common ancestor. Conserved motif analysis suggests a link between all viral PDEs and a similar ancestor among the mammalian AKAP7 proteins despite low levels of sequence conservation. Additionally, we used ancestral sequence reconstruction and structural modeling to reveal that sequence and structural divergence are not well-correlated among these proteins. Specifically, merbecovirus PDEs are as structurally divergent from the ancestral protein and the solved structure of human AKAP7 PDE as they are from each other. In contrast, comparisons of Rotavirus B and G PDEs reveal virtually unchanged structures despite evidence for loss of function in one, suggesting impactful changes that lie outside conserved catalytic sites. These findings highlight the complex and volatile evolutionary history of viral PDEs and provide a framework to facilitate future studies.