Current combination antiretroviral therapies (cART) efficiently suppress HIV-1 reproduction in humans, but the virus persists as integrated proviral reservoirs in small numbers of cells. To generate an antiviral agent capable of eradicating the provirus from infected cells, we employed 145 cycles of substrate-linked directed evolution to evolve a recombinase (Brec1) that site-specifically recognizes a 34-bp sequence present in the long terminal repeats (LTRs) of the majority of the clinically relevant HIV-1 strains and subtypes. Brec1 efficiently, precisely and safely removes the integrated provirus from infected cells and is efficacious on clinical HIV-1 isolates in vitro and in vivo, including in mice humanized with patient-derived cells. Our data suggest that Brec1 has potential for clinical application as a curative HIV-1 therapy.