Immunomodulatory drugs bind to cereblon (CRBN) to confer differentiated substrate specificity on the CRL4(CRBN) E3 ubiquitin ligase. Here we report the identification of a new cereblon modulator, CC-885, with potent anti-tumour activity. The anti-tumour activity of CC-885 is mediated through the cereblon-dependent ubiquitination and degradation of the translation termination factor GSPT1. Patient-derived acute myeloid leukaemia tumour cells exhibit high sensitivity to CC-885, indicating the clinical potential of this mechanism. Crystallographic studies of the CRBN-DDB1-CC-885-GSPT1 complex reveal that GSPT1 binds to cereblon through a surface turn containing a glycine residue at a key position, interacting with both CC-885 and a 'hotspot' on the cereblon surface. Although GSPT1 possesses no obvious structural, sequence or functional homology to previously known cereblon substrates, mutational analysis and modelling indicate that the cereblon substrate Ikaros uses a similar structural feature to bind cereblon, suggesting a common motif for substrate recruitment. These findings define a structural degron underlying cereblon 'neosubstrate' selectivity, and identify an anti-tumour target rendered druggable by cereblon modulation.