Centrioles and cilia are microtubule-based structures, whose precise formation requires controlled cytoplasmic tubulin incorporation. How cytoplasmic tubulin is recognized for centriolar/ciliary-microtubule construction remains poorly understood. Centrosomal-P4.1-associated-protein (CPAP) binds tubulin via its PN2-3 domain. Here, we show that a C-terminal loop-helix in PN2-3 targets β-tubulin at the microtubule outer surface, while an N-terminal helical motif caps microtubule’s α-β surface of β-tubulin. Through this, PN2-3 forms a high-affinity complex with GTP-tubulin, crucial for defining numbers and lengths of centriolar/ciliary-microtubules. Surprisingly, two distinct mutations in PN2-3 exhibit opposite effects on centriolar/ciliary-microtubule lengths. CPAP^F375A, with strongly reduced tubulin interaction, causes shorter centrioles and cilia exhibiting doublet- instead of triplet-microtubules. CPAP^EE343RR that unmasks the β-tubulin polymerization surface displays slightly reduced tubulin-binding affinity inducing over-elongation of newly forming centriolar/ciliary-microtubules by enhanced dynamic release of its bound tubulin. Thus CPAP regulates delivery of its bound-tubulin to define the size of microtubule-based cellular structures using a ‘clutch-like’ mechanism.