The sedimentary basins of Yunnan, Southwest China, record detailed histories of Cenozoic paleoenvironmental change. They track regional tectonic and palaeobiological evolution, both of which are critically important for the development of modern floral diversity in southwestern China and throughout Asia more generally. However, to be useful, the sedimentary archives within the basins have to be placed within a well-constrained timeframe independent of biostratigraphy. Using high resolution U-Pb dating, we redefine the age of fossil-bearing strata in the Wenshan Basin. Regarded as Miocene for the last half century, these basin sediments encompass $30\pm 2$ and $32\pm 1$ Ma early Oligocene tuffaceous horizons, thus indicating a significantly greater antiquity than previously recognized. Together with other regional age revisions our result points to widespread Yunnan basin and orographic development as largely having taken place by the end Paleogene. This age revision provides an important new perspective on the preserved biotas and their evolution in Yunnan, and especially our understanding of the origin of Asian biodiversity which, regionally, had a near-modern composition by the early Oligocene. Crucially, this revised age evidences late Eocene-early Oligocene regional tectonism, pointing to the rise of eastern Tibet and the Hengduan Mountains before the growth of the Himalaya, and that Asia's high plant diversity has a Paleogene origin.