Codanin-1 (CDAN1) is an essential and ubiquitous protein named after congenital dyserythropoietic anemia type I (CDA-I), an autosomal recessive disease that manifests from mutations in the CDAN1 or CDIN1 (CDAN1 interacting nuclease 1) gene. CDAN1 interacts with CDIN1 and the paralogous histone H3-H4 chaperones ASF1A (Anti-Silencing Function 1A) and ASF1B, but its function remains unclear. Here, we biochemically and structurally analyze CDAN1 complexes. We find that CDAN1 dimerizes and assembles into cytosolic complexes with CDIN1 and multiple copies of ASF1A/B. Single-particle cryogenic electron microscopy (cryo-EM) structures of CDAN1 complexes identify interactions with ASF1 mediated by two CDAN1 B-domains commonly found in ASF1 binding partners and two helices that mimic histone H3 binding. We additionally observe that one CDAN1 can recruit two ASF1 molecules and that ASF1A and ASF1B have different requirements for CDAN1 engagement. Our findings explain how CDAN1 sequesters and inhibits the chaperone function of ASF1A/B and provide new molecular-level insights into this enigmatic complex.