Telomeres shorten with each cell division and can ultimately become substrates for nonhomologous end-joining repair, leading to large-scale genomic rearrangements of the kind frequently observed in human cancers. We have characterized more than 1400 telomere fusion events at the single-molecule level, using a combination of high-throughput sequence analysis together with experimentally induced telomeric double-stranded DNA breaks. We show that a single chromosomal dysfunctional telomere can fuse with diverse nontelomeric genomic loci, even in the presence of an otherwise stable genome, and that fusion predominates in coding regions. Fusion frequency was markedly increased in the absence of TP53 checkpoint control and significantly modulated by the cellular capacity for classical, versus alternative, nonhomologous end joining (NHEJ). We observed a striking reduction in inter-chromosomal fusion events in cells lacking DNA ligase 4, in contrast to a remarkably consistent profile of intra-chromosomal fusion in the context of multiple genetic knockouts, including DNA ligase 3 and 4 double-knockouts. We reveal distinct mutational signatures associated with classical NHEJ-mediated inter-chromosomal, as opposed to alternative NHEJ-mediated intra-chromosomal, telomere fusions and evidence for an unanticipated sufficiency of DNA ligase 1 for these intra-chromosomal events. Our findings have implications for mechanisms driving cancer genome evolution.