Repair of DNA double‐stranded breaks (DSBs) is crucial for the maintenance of genome stability. DSBs are repaired by either error prone non‐homologous end‐joining (NHEJ) or error‐free homologous recombination. NHEJ precedes either by a classic, Lig4‐dependent process (C‐NHEJ) or an alternative, Lig4‐independent one (A‐NHEJ). Dysfunctional telomeres arising either through natural attrition due to telomerase deficiency or by removal of telomere‐binding proteins are recognized as DSBs. In this report, we studied which end‐joining pathways are required to join dysfunctional telomeres. In agreement with earlier studies, depletion of Trf2 resulted in end‐to‐end chromosome fusions mediated by the C‐NHEJ pathway. In contrast, removal of Tpp1–Pot1a/b initiated robust chromosome fusions that are mediated by A‐NHEJ. C‐NHEJ is also dispensable for the fusion of naturally shortened telomeres. Our results reveal that telomeres engage distinct DNA repair pathways depending on how they are rendered dysfunctional, and that A‐NHEJ is a major pathway to process dysfunctional telomeres.