ESCRT-III proteins assemble into composite polymers that undergo stepwise changes in composition and structure to deform membranes across the tree of life. Here, using a phylogenetic analysis, we demonstrate that the two endosomal sorting complex required for transport III (ESCRT-III) proteins present in eukaryote's closest Asgard archaeal relatives are evolutionarily related to the B- and A-type eukaryotic paralogs that initiate and execute membrane remodeling, respectively. We show that Asgard ESCRT-IIIB assembles into parallel arrays on planar membranes to initiate membrane deformation, from where it recruits ESCRT-IIIA to generate composite polymers. Last, we show that Asgard ESCRT-IIIA is able to remodel membranes into tubes as a likely prelude to scission. Together, these data reveal a set of conserved principles governing ESCRT-III-dependent membrane remodeling that first emerged in a two-component ESCRT-III system in archaea.