The HIV‐1 transactivation protein (Tat) binds the HIV mRNA transactivation responsive element (TAR), regulating transcription and reactivation from latency. Drugs against Tat are unfortunately not clinically available. We reported that didehydro‐cortistatin A (dCA) inhibits HIV‐1 Tat activity. In human CD4+ T cells isolated from aviremic individuals and in the humanized mouse model of latency, combining dCA with antiretroviral therapy accelerates HIV‐1 suppression and delays viral rebound upon treatment interruption. This drug class is amenable to block‐and‐lock functional cure approaches, aimed at a durable state of latency. Simian immunodeficiency virus (SIV) infection of rhesus macaques (RhMs) is the best‐characterized model for AIDS research. Here, we demonstrate, using in vitro and cell‐based assays, that dCA directly binds to SIV Tat's basic domain. dCA specifically inhibits SIV Tat binding to TAR, but not a Tat‐Rev fusion protein, which activates transcription when Rev binds to its cognate RNA binding site replacing the apical region of TAR. Tat‐TAR inhibition results in loss of RNA polymerase II recruitment to the SIV promoter. Importantly, dCA potently inhibits SIV reactivation from latently infected Hut78 cells and from primary CD4+ T cells explanted from SIVmac239‐infected RhMs. In sum, dCA's remarkable breadth of activity encourages SIV‐infected RhM use for dCA preclinical evaluation.—Mediouni, S., Kessing, C. F., Jablonski, J. A., Thenin‐Houssier, S., Clementz, M., Kovach, M. D., Mousseau, G., de Vera, I.M.S., Li, C., Kojetin, D. J., Evans, D. T., Valente, S. T. The Tat inhibitor didehydro‐cortistatin A suppresses SIV replication and reactivation. FASEB J. 33, 8280–8293 (2019). http://www.fasebj.org