African horse sickness virus (AHSV), a member of the orbivirus genus of the family Reoviridae, is an insect-vectored pathogen of horses of concern to the equine industry. Studies on AHSV replication and pathogenesis have been hampered by the lack of reverse genetics allowing targeted mutation of viral genomes. We demonstrate that AHSV single-stranded RNA synthesized in vitro (core transcripts) is infectious and that there are distinct primary and secondary stages of the replication cycle. Transfection with a mixture of core transcripts from two different serotypes or a mixture of core transcripts and a T7 derived transcript resulted in the recovery of reassortant viruses. Recovery of infectious ASHV from nucleic acid will benefit investigation of the virus and the generation of attenuated vaccines.