Centrosomes are non-membrane-bound compartments that nucleate microtubule arrays. They consist of nanometer-scale centrioles surrounded by a micron-scale, dynamic assembly of protein called the pericentriolar material (PCM). To study how PCM forms a spherical compartment that nucleates microtubules, we reconstituted PCM-dependent microtubule nucleation in vitro using recombinant C. elegans proteins. We found that macromolecular crowding drives phase separation of the key PCM scaffold protein SPD-5 into spherical droplets that morphologically and dynamically resemble in vivo PCM. These SPD-5 droplets recruited the microtubule polymerase ZYG-9 (XMAP215 homologue) and the microtubule-stabilizing protein TPXL-1 (TPX2 homologue). Together, these three proteins concentrated tubulin ~4-fold over background, which was sufficient to reconstitute nucleation of microtubule asters in vitro. Our results suggest that in vivo PCM is a selective phase that organizes microtubule arrays through localized concentration of tubulin by microtubule effector proteins.