How cellular organelles assemble is a fundamental question in biology. The centriole organelle organizes around a nine-fold symmetrical cartwheel structure typically ∼100 nm high comprising a stack of rings that each accommodates nine homodimers of SAS-6 proteins. Whether nine-fold symmetrical ring-like assemblies of SAS-6 proteins harbour more peripheral cartwheel elements is unclear. Furthermore, the mechanisms governing ring stacking are not known. Here we develop a cell-free reconstitution system for core cartwheel assembly. Using cryo-electron tomography, we uncover that the Chlamydomonas reinhardtii proteins CrSAS-6 and Bld10p together drive assembly of the core cartwheel. Moreover, we discover that CrSAS-6 possesses autonomous properties that ensure self-organized ring stacking. Mathematical fitting of reconstituted cartwheel height distribution suggests a mechanism whereby preferential addition of pairs of SAS-6 rings governs cartwheel growth. In conclusion, we have developed a cell-free reconstitution system that reveals fundamental assembly principles at the root of centriole biogenesis.