Poxviruses encode their own type IB topoisomerases (TopIBs), which release superhelical tension generated by replication and transcription of their genomes. To investigate the reaction catalyzed by viral TopIBs, we have determined the structure of a variola virus topoisomerase-DNA complex trapped as a vanadate transition state mimic. The structure reveals how the viral TopIB enzymes are likely to position the DNA duplex for ligation following relaxation of supercoils and identifies the sources of friction observed in single-molecule experiments that argue against free rotation. The structure also identifies a conformational change in the leaving group sugar that must occur prior to cleavage and reveals a mechanism for promoting ligation following relaxation of supercoils that involves an Asp-minor groove interaction. Overall, the new structural data support a common catalytic mechanism for the TopIB superfamily but indicate distinct methods for controlling duplex rotation in the small versus large enzyme subfamilies.