The conserved N-terminal domains of the major tegument proteins of herpes viridae encode cysteine proteases with potent ubiquitin and NEDD8-specific deconjugase activity. Here we show that the Epstein-Barr virus-encoded member of this enzyme family, BPLF1, is targeted to cullin-RING ubiquitin ligases (CRLs) via the interaction of the conserved helix-2 with helix-23 of the C-terminal domain (CTD) of cullins, at a site involved in electrostatic interaction with helix-8 of the CRL regulator CAND1. Mutation of the solvent-exposed Asp86 and Asp90 of helix-2 to Arg does not affect the enzymatic activity of BPLF1 but abolishes cullin binding and prevents CRL inactivation. The binding of the catalytically active BPLF1 to cullins inhibits the recruitment of CAND1 to the deneddylated CRLs and promotes the selective degradation of cullins by the proteasome. Cullin proteolysis is rescued by the overexpression of CAND1 or its CTD-binding N-terminal domain. These findings illustrate a new strategy for viral modulation of CRL activity where the combined effects of cullin deneddylation and their targeting for proteasomal degradation drive stable inactivation of the ligases.