Polyploidy often confers emergent properties, such as the higher fibre productivity and quality of tetraploid cottons than diploid cottons bred for the same environments1. Here we show that an abrupt five- to sixfold ploidy increase approximately 60 million years (Myr) ago, and allopolyploidy reuniting divergentGossypiumgenomes approximately 1–2 Myr ago2, conferred about 30–36-fold duplication of ancestral angiosperm (flowering plant) genes in elite cottons (Gossypium hirsutumandGossypium barbadense), genetic complexity equalled only byBrassica3among sequenced angiosperms. Nascent fibre evolution, before allopolyploidy, is elucidated by comparison of spinnable-fibredGossypium herbaceumA and non-spinnableGossypium longicalyxF genomes to one another and the outgroup D genome of non-spinnableGossypium raimondii. The sequence of aG. hirsutumAtDt (in which ‘t’ indicates tetraploid) cultivar reveals many non-reciprocal DNA exchanges between subgenomes that may have contributed to phenotypic innovation and/or other emergent properties such as ecological adaptation by polyploids. Most DNA-level novelty inG. hirsutumrecombines alleles from the D-genome progenitor native to its New World habitat and the Old World A-genome progenitor in which spinnable fibre evolved. Coordinated expression changes in proximal groups of functionally distinct genes, including a nuclear mitochondrial DNA block, may account for clusters of cotton-fibre quantitative trait loci affecting diverse traits. Opportunities abound for dissecting emergent properties of other polyploids, particularly angiosperms, by comparison to diploid progenitors and outgroups.