Histone modifications perform a vast array of functions in regulating gene expression, DNA replication, and repair. Monoubiquitination of histone H2B at K123 in yeast (K120 in humans) is an intriguing modification because it is deposited cotranscriptionally, mediates the installation of several other epigenetic marks, and then disappears; hence, it is associated transiently with actively transcribed chromatin. In yeast, the H2B ubiquitin writer is the E2/E3 pair Rad6/Bre1, and there are two deubiquitinases that can erase it, Ubp8 and Ubp10. Whilst Ubp8 resides within the larger SAGA complex, Ubp10 (USP36 in humans) is a monomeric and constitutively active deubiquitinase, raising questions as to what processes regulate it, given it would be undesirable for H2B to be deubiquitinated prematurely before downstream processes connected to this epigenetic mark occur. Here we show that Ubp10’s activity is regulated by acidic regions within its long N-terminal intrinsically disordered region (IDR), which extensively interact with H2A/H2B dimers, as shown by crosslinking mass spectrometry. These interactions vanish when H2A/H2B is present in nucleosomes. These observations explain why Ubp10 has low baseline activity on nucleosomes, but is activated by FACT, a histone chaperone which evicts H2A/H2B dimers from nucleosomes, thereby generating Ubp10’s preferred substrate, which we demonstrate with single molecule fluorescence experiments. Hence, this work provides a biophysical mechanism for how Ubp10 can provide a housekeeping function to deubiquitinate actively-transcribed DNA, wherein FACT produces a temporary pool of H2A/H2B dimers.