Atomically precise metal nanoclusters (NCs) have become an important class of catalysts due to their catalytic activity, high surface area, and tailored active sites. However, the design and development of bond-forming reaction catalysts based on copper NCs are still in their early stages. Herein, we report the synthesis of an atomically precise copper nanocluster with a planar core and unique shell, [Cu45(TBBT)29(TPP)4(C4H11N)2H14]2+ (Cu45) (TBBT: 4-tert-butylbenzenethiol; TPP: triphenylphosphine), in high yield via a one-pot reduction method. The resulting structurally well-defined Cu45 is a highly efficient catalyst for the hydroboration reaction of alkynes and alkenes. Mechanistic studies show that a single-electron oxidation of the in situ-formed ate complex enables the hydroboration via the formation of boryl-centered radicals under mild conditions. This work demonstrates the promise of tailored copper nanoclusters as catalysts for C–B heteroatom bond-forming reactions. The catalysts are compatible with a wide range of alkynes and alkenes and functional groups for producing hydroborated products.