Assembly of an integral Golgi complex is driven by microtubule (MT)-dependent transport. Conversely, the Golgi itself functions as an unconventional MT-organizing center (MTOC). This raises the question of whether Golgi assembly requires centrosomal MTs or can be self-organized, relying on its own MTOC activity. The computational model presented here predicts that each MT population is capable of gathering Golgi stacks but not of establishing Golgi complex integrity or polarity. In contrast, the concerted effort of two MT populations would assemble an integral, polarized Golgi complex. Indeed, while laser ablation of the centrosome did not alter already-formed Golgi complexes, acentrosomal cells fail to reassemble an integral complex upon nocodazole washout. Moreover, polarity of post-Golgi trafficking was compromised under these conditions, leading to strong deficiency in polarized cell migration. Our data indicate that centrosomal MTs complement Golgi self-organization for proper Golgi assembly and motile-cell polarization.