Long-lasting, latently infected resting CD4⁺ T cells are the greatest obstacle to obtaining a cure for HIV infection, as these cells can persist despite decades of treatment with antiretroviral therapy (ART). Estimates indicate that more than 70 years of continuous, fully suppressive ART are needed to eliminate the HIV reservoir. Alternatively, induction of HIV from its latent state could accelerate the decrease in the reservoir, thus reducing the time to eradication. Previous attempts to reactivate latent HIV in preclinical animal models and in clinical trials have measured HIV induction in the peripheral blood with minimal focus on tissue reservoirs and have had limited effect^{, , , , , , –}. Here we show that activation of the non-canonical NF-κB signalling pathway by AZD5582 results in the induction of HIV and SIV RNA expression in the blood and tissues of ART-suppressed bone-marrow–liver–thymus (BLT) humanized mice and rhesus macaques infected with HIV and SIV, respectively. Analysis of resting CD4⁺ T cells from tissues after AZD5582 treatment revealed increased SIV RNA expression in the lymph nodes of macaques and robust induction of HIV in almost all tissues analysed in humanized mice, including the lymph nodes, thymus, bone marrow, liver and lung. This promising approach to latency reversal—in combination with appropriate tools for systemic clearance of persistent HIV infection—greatly increases opportunities for HIV eradication.