Genome rearrangements often result from non-allelic homologous recombination (NAHR) between repetitive DNA elements dispersed throughout the genome. Here we systematically analyze NAHR between Ty retrotransposons using a genome-wide approach that exploits unique features of Saccharomyces cerevisiae purebred and Saccharomyces cerevisiae/Saccharomyces bayanus hybrid diploids. We find that DNA double-strand breaks (DSBs) induce NAHR-dependent rearrangements using Ty elements located 12 to 48 kilobases distal to the break site. This break-distal recombination (BDR) occurs frequently, even when allelic recombination can repair the break using the homolog. Robust BDR-dependent NAHR demonstrates that sequences very distal to DSBs can effectively compete with proximal sequences for repair of the break. In addition, our analysis of NAHR partner choice between Ty repeats shows that intrachromosomal Ty partners are preferred despite the abundance of potential interchromosomal Ty partners that share higher sequence identity. This competitive advantage of intrachromosomal Tys results from the relative efficiencies of different NAHR repair pathways. Finally, NAHR generates deleterious rearrangements more frequently when DSBs occur outside rather than within a Ty repeat. These findings yield insights into mechanisms of repeat-mediated genome rearrangements associated with evolution and cancer.