Chromosomal rearrangements are a major driver of eukaryotic genome evolution, affecting speciation, pathogenicity and cancer progression. Changes in chromosome structure are often initiated by mis-repair of double-strand breaks in the DNA. Mis-repair is particularly likely when telomeres are lost or when dispersed repeats misalign during crossing-over. Fungi carry highly polymorphic chromosomal complements showing substantial variation in chromosome length and number. The mechanisms driving chromosome polymorphism in fungi are poorly understood. We aimed to identify mechanisms of chromosomal rearrangements in the fungal wheat pathogen Zymoseptoria tritici. We combined population genomic resequencing and chromosomal segment PCR assays with electrophoretic karyotyping and resequencing of parents and offspring from experimental crosses to show that this pathogen harbors a highly diverse complement of accessory chromosomes that exhibits strong global geographic differentiation in numbers and lengths of chromosomes. Homologous chromosomes carried highly differentiated gene contents due to numerous insertions and deletions. The largest accessory chromosome recently doubled in length through insertions totaling 380 kb. Based on comparative genomics, we identified the precise breakpoint locations of these insertions. Nondisjunction during meiosis led to chromosome losses in progeny of three different crosses. We showed that a new accessory chromosome emerged in two viable offspring through a fusion between sister chromatids. Such chromosome fusion is likely to initiate a breakage-fusion-bridge (BFB) cycle that can rapidly degenerate chromosomal structure. We suggest that the accessory chromosomes of Z. tritici originated mainly from ancient core chromosomes through a degeneration process that included BFB cycles, nondisjunction and mutational decay of duplicated sequences. The rapidly evolving accessory chromosome complement may serve as a cradle for adaptive evolution in this and other fungal pathogens.