Flowering plants (angiosperms) are the most diverse of all land plants, becoming abundant in the Cretaceous and achieving dominance in the Cenozoic. However, the exact timing of their origin remains a controversial topic, with molecular clocks generally placing their origin much further back in time than the oldest unequivocal fossils. To resolve this discrepancy, we developed a Bayesian method to estimate the ages of angiosperm families on the basis of the fossil record (a newly compiled dataset of ~15,000 occurrences in 198 families) and their living diversity. Our results indicate that several families originated in the Jurassic, strongly rejecting a Cretaceous origin for the group. We report a marked increase in lineage accumulation from 125 to 72 million years ago, supporting Darwin's hypothesis of a rapid Cretaceous angiosperm diversification. Our results demonstrate that a pre-Cretaceous origin of angiosperms is supported not only by molecular clock approaches but also by analyses of the fossil record that explicitly correct for incomplete sampling.