One in four women suffers from uterine leiomyomas (ULs)—benign tumours of the uterine wall, also known as uterine fibroids—at some point in premenopausal life. ULs can cause excessive bleeding, pain and infertility, and are a common cause of hysterectomy. They emerge through at least three distinct genetic drivers: mutations in MED12 or FH, or genomic rearrangement of HMGA2. Here we created genome-wide datasets, using DNA, RNA, assay for transposase-accessible chromatin (ATAC), chromatin immunoprecipitation (ChIP) and HiC chromatin immunoprecipitation (HiChIP) sequencing of primary tissues to profoundly understand the genesis of UL. We identified somatic mutations in genes encoding six members of the SRCAP histone-loading complex, and found that germline mutations in the SRCAP members YEATS4 and ZNHIT1 predispose women to UL. Tumours bearing these mutations showed defective deposition of the histone variant H2A.Z. In ULs, H2A.Z occupancy correlated positively with chromatin accessibility and gene expression, and negatively with DNA methylation, but these correlations were weak in tumours bearing SRCAP complex mutations. In these tumours, open chromatin emerged at transcription start sites where H2A.Z was lost, which was associated with upregulation of genes. Furthermore, YEATS4 defects were associated with abnormal upregulation of bivalent embryonic stem cell genes, as previously shown in mice. Our work describes a potential mechanism of tumorigenesis—epigenetic instability caused by deficient H2A.Z deposition—and suggests that ULs arise through an aberrant differentiation program driven by deranged chromatin, emanating from a small number of mutually exclusive driver mutations.