Acetylation of histones and transcription-related factors is known to exert epigenetic and transcriptional control of gene expression. Here we report that histone acetyltransferases (HATs) and histone deacetylases (HDACs) also regulate gene expression at the posttranscriptional level by controlling poly(A) RNA stability. Inhibition of HDAC1 and HDAC2 induces massive and widespread degradation of normally stable poly(A) RNA in mammalian and Drosophila cells. Acetylation-induced RNA decay depends on the HATs p300 and CBP, which acetylate the exoribonuclease CAF1a, a catalytic subunit of the CCR4-CAF1-NOT deadenlyase complex and thereby contribute to accelerating poly(A) RNA degradation. Taking adipocyte differentiation as a model, we observe global stabilization of poly(A) RNA during differentiation, concomitant with loss of CBP/p300 expression. Our study uncovers reversible acetylation as a fundamental switch by which HATs and HDACs control the overall turnover of poly(A) RNA.