Resolution of four-way Holliday junctions is a critical intermediate step of homologous recombination. DNA junctions must be processed by abundant junction-resolving endonucleases to cleave the covalent link between two chromosomes. Although the catalytic activity and interaction mode of endonucleases with Holliday junction have been characterized in great detail by biochemical and structural studies, it remains unclear how the enzymes find their substrate located within kilobase pairs of duplex DNA. Here, we present a complete single-molecule reaction trajectory for a junction-resolving enzyme finding and cleaving a Holliday junction. We employed correlative optical tweezers with confocal fluorescence microscopy to track a single dimer of endonuclease I on the DNA template in real-time. We observed that the enzyme binds remotely to the dsDNA and then undergoes 1D diffusion. Upon encountering the four-way junction, a catalytically impaired endonuclease I mutant remains bound at that point for long periods. An active enzyme, however, cleaves the junction after a few seconds. When an N-terminal truncated endonuclease mutant is used, the enzyme fails to diffuse along dsDNA and dissociates after short periods of time, indicating that DNA encirclement by the disordered N-terminus is a key requirement for 1D diffusion and efficient target localisation. Quantitative analysis of each of these stages revealed a comprehensive description of the facilitated diffusion mechanism. We show that the eukaryotic junction-resolving enzyme GEN1 also undergoes facilitated diffusion on dsDNA until it becomes located at a junction, so that the general resolution trajectory is likely to be applicable to most junction resolving enzymes.