The deubiquitinating enzyme BAP1 is an important tumor suppressor that has drawn attention in the clinic since its loss leads to a variety of cancers. BAP1 is activated by ASXL1 to deubiquitinate mono-ubiquitinated H2A at K119 in Polycomb gene repression, but the mechanism of this reaction remains poorly defined. Here we show that the BAP1 C-terminal extension is important for H2A deubiquitination by auto-recruiting BAP1 to nucleosomes in a process that does not require the nucleosome acidic patch. This initial encounter-like complex is unproductive and needs to be activated by the DEUBAD domains of ASXL1, ASXL2 or ASXL3 to increase BAP1's affinity for ubiquitin on H2A, to drive the deubiquitination reaction. The reaction is specific for Polycomb modifications of H2A as the complex cannot deubiquitinate the DNA damage-dependent ubiquitination at H2A K13/15. Our results contribute to the molecular understanding of this important tumor suppressor.