DNA gyrase is a type II topoisomerase with the unique capacity to introduce negative supercoiling in DNA. In bacteria, DNA gyrase has an essential role in the homeostatic regulation of supercoiling. While ubiquitous in bacteria, DNA gyrase was previously reported to have a patchy distribution in Archaea but its emergent function and evolutionary history in this domain of life remains elusive. In this study, we used phylogenomic approaches and an up-to date sequence dataset to establish global and archaea-specific phylogenies of DNA gyrases. The most parsimonious evolutionary scenario infers that DNA gyrase was introduced into the lineage leading to Euryarchaeal group II via a single horizontal gene transfer from a bacterial donor which we identified as an ancestor of Gracilicutes and/or Terrabacteria. The archaea-focused trees indicate that DNA gyrase spread from Euryarchaeal group II to some DPANN and Asgard lineages via rare horizontal gene transfers. The analysis of successful recent transfers suggests a requirement for syntropic or symbiotic/parasitic relationship between donor and recipient organisms. We further show that the ubiquitous archaeal Topoisomerase VI may have co-evolved with DNA gyrase to allow the division of labor in the management of topological constraints. Collectively, our study reveals the evolutionary history of DNA gyrase in Archaea and provides testable hypotheses to understand the prerequisites for successful establishment of DNA gyrase in a naive archaeon and the associated adaptations in the management of topological constraints.