The ubiquitin E3 ligase substrate adapter cereblon (CRBN) is a target of thalidomide and lenalidomide1, therapeutic agents used in the treatment of haematopoietic malignancies2-4 and as ligands for targeted protein degradation5-7. These agents are proposed to mimic a naturally occurring degron; however, the structural motif recognized by the thalidomide-binding domain of CRBN remains unknown. Here we report that C-terminal cyclic imides, post-translational modifications that arise from intramolecular cyclization of glutamine or asparagine residues, are physiological degrons on substrates for CRBN. Dipeptides bearing the C-terminal cyclic imide degron substitute for thalidomide when embedded within bifunctional chemical degraders. Addition of the degron to the C terminus of proteins induces CRBN-dependent ubiquitination and degradation in vitro and in cells. C-terminal cyclic imides form adventitiously on physiologically relevant timescales throughout the human proteome to afford a degron that is endogenously recognized and removed by CRBN. The discovery of the C-terminal cyclic imide degron defines a regulatory process that may affect the physiological function and therapeutic engagement of CRBN.