Epigenetic modulators of the histone deacetylase (HDAC) family control key biological processes and are frequently dysregulated in cancer. There is superior activity of HDAC inhibitors (HDACi) in patients with myeloproliferative neoplasms (MPNs) that carry the Janus kinase-2 point mutant JAK2(V617F). This constitutively active tyrosine kinase activates signal-transducer-and-activator-of-transcription (STAT) transcription factors to promote cell proliferation and inflammatory processes. We reveal that the inhibition of HDAC1/HDAC2 with the clinically advanced HDACi romidepsin, the experimental HDACi entinostat and MERCK60, and genetic depletion of HDAC1/HDAC2 induce apoptosis and long-term growth arrest of primary and permanent MPN cells in vitro and in vivo. This treatment spares normal hematopoietic stem cells and does not compromise blood cell differentiation. At the molecular level, HDAC1 and HDAC2 control the protein stability of SIAH2 through acetylation. Genetic knockout experiments show that SIAH2 accelerates the proteasomal degradation of JAK2(V617F) in conjunction with the E2 ubiquitin-conjugating enzyme UBCH8. SIAH2 binds to the surface-exposed SIAH degron motif VLP1002 in the catalytic domain of JAK2(V617F). At the functional level, SIAH2 knockout MPN cells are significantly less sensitive to HDACi. Global RNA sequencing verifies that JAK-STAT signaling is a prime target of SIAH2. Moreover, HDAC1 is an adverse prognostic factor in patients with acute myeloid leukemia (n = 150, p = 0.02), being a possible complication of MPNs. These insights reveal a previously unappreciated link between HDAC1/HDAC2 as key molecular targets, the still undefined regulation of cytoplasmic-to-nuclear signaling by HDACs, and how HDACi kill JAK2(V617F)-positive cells from MPN patients and mice with JAK2(V617F) in vitro and in vivo.