Bluetongue virus (BTV) is a vector-borne, nonenveloped icosahedral particle that is organized in two capsids, an outer capsid of two proteins, VP2 and VP5, and an inner capsid (or core) composed of two major proteins, VP7 and VP3, in two layers. The VP3 layer (subcore) encloses viral transcription complex (VP1 polymerase, VP4 capping enzyme, VP6 helicase) and a 10-segmented double-stranded (dsRNA) genome. Although much is known about the BTV capsids, the order of the core assembly and the mechanism of genome packaging remain unclear. Here, we established a cell-free system to reconstitute subcore and core structures with the proteins and ssRNAs, demonstrating that reconstituted cores are infectious in insect cells. Furthermore, we showed that the BTV ssRNAs are essential to drive the assembly reaction and that there is a distinct order of internal protein recruitment during the assembly process. The in vitro engineering of infectious BTV cores is unique for any member of the Reoviridae and will facilitate future studies of RNA-protein interactions during BTV core assembly.