The chromosomal theory of inheritance has dominated human genetics, including cancer genetics. Genes on the same chromosome segregate together while genes on different chromosomes assort independently, providing a fundamental tenet of Mendelian inheritance. Extrachromosomal DNA (ecDNA) is a frequent event in cancer that drives oncogene amplification, dysregulated gene expression and intratumoral heterogeneity, including through random segregation during cell division. Distinct ecDNA sequences, herein termed ecDNA species, can co-exist to facilitate intermolecular cooperation in cancer cells. However, how multiple ecDNA species within a tumor cell are assorted and maintained across somatic cell generations to drive cancer cell evolution is not known. Here we show that cooperative ecDNA species can be coordinately inherited through mitotic co-segregation. Imaging and single-cell analyses show that multiple ecDNAs encoding distinct oncogenes co-occur and are correlated in copy number in human cancer cells. EcDNA species are coordinately segregated asymmetrically during mitosis, resulting in daughter cells with simultaneous copy number gains in multiple ecDNA species prior to any selection. Computational modeling reveals the quantitative principles of ecDNA co-segregation and co-selection, predicting their observed distributions in cancer cells. Finally, we show that coordinated inheritance of ecDNAs enables co-amplification of specialized ecDNAs containing only enhancer elements and guides therapeutic strategies to jointly deplete cooperating ecDNA oncogenes. Coordinated inheritance of ecDNAs confers stability to oncogene cooperation and novel gene regulatory circuits, allowing winning combinations of epigenetic states to be transmitted across cell generations.