Persistence of latent, replication-competent Human Immunodeficiency Virus type 1 (HIV-1) provirus is the main impediment towards a cure for HIV/AIDS (Acquired Immune Deficiency Syndrome). Therefore, different therapeutic strategies to eliminate the viral reservoirs are currently being explored. We here propose a novel strategy to reduce the replicating HIV reservoir during primary HIV infection by means of drug-induced retargeting of HIV integration. A novel class of integration inhibitors, referred to as LEDGINs, inhibit the interaction between HIV integrase and the LEDGF/p75 host cofactor, the main determinant of lentiviral integration site selection. We show for the first time that LEDGF/p75 depletion hampers HIV-1 reactivation in cell culture. Next we demonstrate that LEDGINs relocate and retarget HIV integration resulting in a HIV reservoir that is refractory to reactivation by different latency-reversing agents. Taken together, these results support the potential of integrase inhibitors that modulate integration site targeting to reduce the likeliness of viral rebound.