Higher-order structures of the microtubule (MT) cytoskeleton are comprised of two architectures: bundles and asters. Although both architectures are critical for cellular function, the molecular pathways that drive aster formation are poorly understood. Here, we study aster formation by human minus-end-directed kinesin-14 (HSET/KIFC1). We show that HSET is incapable of forming asters from preformed, nongrowing MTs, but rapidly forms MT asters in the presence of soluble (non-MT) tubulin. HSET binds soluble (non-MT) tubulin via its N-terminal tail domain to form heterogeneous HSET-tubulin clusters containing multiple motors. Cluster formation induces motor processivity and rescues the formation of asters from nongrowing MTs. We then show that excess soluble (non-MT) tubulin stimulates aster formation in HeLa cells overexpressing HSET during mitosis. We propose a model where HSET can toggle between MT bundle and aster formation in a manner governed by the availability of soluble (non-MT) tubulin.