Mitochondria have a major role in energy production via oxidative phosphorylation, which is dependent on the expression of critical genes encoded by mitochondrial (mt)DNA. Mutations in mtDNA can cause fatal or severely debilitating disorders with limited treatment options. Clinical manifestations vary based on mutation type and heteroplasmy (that is, the relative levels of mutant and wild-type mtDNA within each cell). Here we generated genetically corrected pluripotent stem cells (PSCs) from patients with mtDNA disease. Multiple induced pluripotent stem (iPS) cell lines were derived from patients with common heteroplasmic mutations including 3243A>G, causing mitochondrial encephalomyopathy and stroke-like episodes (MELAS), and 8993T>G and 13513G>A, implicated in Leigh syndrome. Isogenic MELAS and Leigh syndrome iPS cell lines were generated containing exclusively wild-type or mutant mtDNA through spontaneous segregation of heteroplasmic mtDNA in proliferating fibroblasts. Furthermore, somatic cell nuclear transfer (SCNT) enabled replacement of mutant mtDNA from homoplasmic 8993T>G fibroblasts to generate corrected Leigh-NT1 PSCs. Although Leigh-NT1 PSCs contained donor oocyte wild-type mtDNA (human haplotype D4a) that differed from Leigh syndrome patient haplotype (F1a) at a total of 47 nucleotide sites, Leigh-NT1 cells displayed transcriptomic profiles similar to those in embryo-derived PSCs carrying wild-type mtDNA, indicative of normal nuclear-to-mitochondrial interactions. Moreover, genetically rescued patient PSCs displayed normal metabolic function compared to impaired oxygen consumption and ATP production observed in mutant cells. We conclude that both reprogramming approaches offer complementary strategies for derivation of PSCs containing exclusively wild-type mtDNA, through spontaneous segregation of heteroplasmic mtDNA in individual iPS cell lines or mitochondrial replacement by SCNT in homoplasmic mtDNA-based disease.