The Human T-cell leukaemia virus type 1 (HTLV-1) is a pathogenic retrovirus that persists as a provirus in the genome of infected cells and can lead to adult T-cell leukaemia (ATL). Worldwide, more than 10 million people are infected and approximately 5% of these individuals will develop ATL, a highly aggressive cancer that is currently incurable. In the last years, genome editing tools have emerged as promising antiviral agents. In this proof-of-concept study, we used substrate linked directed evolution (SLiDE) to engineer Cre-derived site-specific recombinases to excise the HTLV-1 proviral genome from infected cells. We identified a conserved loxP-like sequence (loxHTLV) present in the long terminal repeats of the majority of virus isolates. After 181 cycles of SLiDE, we isolated a designer-recombinase (designated RecHTLV), which efficiently recombines the loxHTLV sequence in bacteria and human cells with high specificity. Expression of RecHTLV in human Jurkat T-cells resulted in antiviral activity when challenged with an HTLV-1 infection. Moreover, expression of RecHTLV in chronically infected SP cells led to the excision of HTLV-1 proviral DNA. Our data suggest that recombinase mediated excision of the HTLV-1 provirus represents a promising approach to reduce proviral load in HTLV-1 infected individuals, potentially preventing the development of HTLV-1 associated diseases.