Sarcomas are cancers of the bone and soft tissue often defined by gene fusions. Ewing sarcoma involves fusions between EWSR1, a gene encoding an RNA binding protein, and E26 transformation-specific (ETS) transcription factors. We explored how and when EWSR1-ETS fusions arise by studying the whole genomes of Ewing sarcomas. In 52 of 124 (42%) of tumors, the fusion gene arises by a sudden burst of complex, loop-like rearrangements, a process called chromoplexy, rather than by simple reciprocal translocations. These loops always contained the disease-defining fusion at the center, but they disrupted multiple additional genes. The loops occurred preferentially in early replicating and transcriptionally active genomic regions. Similar loops forming canonical fusions were found in three other sarcoma types. Chromoplexy-generated fusions appear to be associated with an aggressive form of Ewing sarcoma. These loops arise early, giving rise to both primary and relapse Ewing sarcoma tumors, which can continue to evolve in parallel.