Relapse of acute myeloid leukemia (AML) is highly aggressive and often treatment refractory. We analyzed previously published AML relapse cohorts and found that 40% of relapses occur without changes in driver mutations, suggesting that non-genetic mechanisms drive relapse in a large proportion of cases. We therefore characterized epigenetic patterns of AML relapse using 26 matched diagnosis-relapse samples with ATAC-seq. This analysis identified a relapse-specific chromatin accessibility signature for mutationally stable AML, suggesting that AML undergoes epigenetic evolution at relapse independent of mutational changes. Analysis of leukemia stem cell (LSC) chromatin changes at relapse indicated that this leukemic compartment underwent significantly less epigenetic evolution than non-LSCs, while epigenetic changes in non-LSCs reflected overall evolution of the bulk leukemia. Finally, we used single-cell ATAC-seq paired with mitochondrial sequencing (mtscATAC) to map clones from diagnosis into relapse along with their epigenetic features. We found that distinct mitochondrially-defined clones exhibit more similar chromatin accessibility at relapse relative to diagnosis, demonstrating convergent epigenetic evolution in relapsed AML. These results demonstrate that epigenetic evolution is a feature of relapsed AML and that convergent epigenetic evolution can occur following treatment with induction chemotherapy.