Centrioles have a unique, conserved architecture formed by three linked, ‘triplet’, microtubules arranged in ninefold symmetry. The mechanisms by which these triplet microtubules are formed remain unclear but likely involve the noncanonical tubulins delta-tubulin and epsilon-tubulin. Previously, we found that human cells lacking delta-tubulin or epsilon-tubulin form abnormal centrioles, characterized by an absence of triplet microtubules, lack of central core protein POC5, and a futile cycle of centriole formation and disintegration (Wang et al., 2017). Here, we show that human cells lacking either TEDC1 or TEDC2 have similar abnormalities. Using ultrastructure expansion microscopy, we observed that mutant centrioles elongate to the same length as control centrioles in G2 phase and fail to recruit central core scaffold proteins. Remarkably, mutant centrioles also have an expanded proximal region. During mitosis, these mutant centrioles further elongate before fragmenting and disintegrating. All four proteins physically interact and TEDC1 and TEDC2 can form a subcomplex in the absence of the tubulins, supporting an AlphaFold Multimer model of the tetramer. TEDC1 and TEDC2 localize to centrosomes and are mutually dependent on each other and on delta-tubulin and epsilon-tubulin for localization. Our results demonstrate that delta-tubulin, epsilon-tubulin, TEDC1, and TEDC2 function together to promote robust centriole architecture, laying the foundation for future studies on the mechanisms underlying the assembly of triplet microtubules and their interactions with centriole structure.