Single-stranded (ss)DNA viruses are extremely widespread, infect diverse hosts from all three domains of life and include important pathogens. Most ssDNA viruses possess small genomes that replicate by the rolling-circle-like mechanism initiated by a distinct virus-encoded endonuclease. However, viruses of the family Bidnaviridae, instead of the endonuclease, encode a protein-primed type B DNA polymerase (PolB) and hence break this pattern. We investigated the provenance of all bidnavirus genes and uncover an unexpected turbulent evolutionary history of these unique viruses. Our analysis strongly suggests that bidnaviruses evolved from a parvovirus ancestor from which they inherit a jelly-roll capsid protein and a superfamily 3 helicase. The radiation of bidnaviruses from parvoviruses was probably triggered by integration of the ancestral parvovirus genome into a large virus-derived DNA transposon of the Polinton (polintovirus) family resulting in the acquisition of the polintovirus PolB gene along with terminal inverted repeats. Bidnavirus genes for a receptor-binding protein and a potential novel antiviral defense modulator are derived from dsRNA viruses (Reoviridae) and dsDNA viruses (Baculoviridae), respectively. The unusual evolutionary history of bidnaviruses emphasizes the key role of horizontal gene transfer, sometimes between viruses with completely different genomes but occupying the same niche, in the emergence of new viral types.