Ubiquitination controls the stability of most cellular proteins, and its deregulation contributes to human diseases including cancer. Deubiquitinases remove ubiquitin from proteins, and their inhibition can induce the degradation of selected proteins, potentially including otherwise ‘undruggable’ targets. For example, the inhibition of ubiquitin-specific protease 7 (USP7) results in the degradation of the oncogenic E3 ligase MDM2, and leads to re-activation of the tumour suppressor p53 in various cancers. Here we report that two compounds, FT671 and FT827, inhibit USP7 with high affinity and specificity in vitro and within human cells. Co-crystal structures reveal that both compounds target a dynamic pocket near the catalytic centre of the auto-inhibited apo form of USP7, which differs from other USP deubiquitinases. Consistent with USP7 target engagement in cells, FT671 destabilizes USP7 substrates including MDM2, increases levels of p53, and results in the transcription of p53 target genes, induction of the tumour suppressor p21, and inhibition of tumour growth in mice.