Differences in species richness between regions are ultimately explained by patterns of speciation, extinction, and biogeographic dispersal. Yet, few studies have considered the role of all three processes in generating the high biodiversity of tropical regions. A recent study of a speciose group of predominately New World frogs (Hylidae) showed that their low diversity in temperate regions was associated with relatively recent colonization of these regions, rather than latitudinal differences in diversification rates (rates of speciation-extinction). Here, we perform parallel analyses on the most species-rich group of Old World frogs (Ranidae; approximately 1300 species) to determine if similar processes drive the latitudinal diversity gradient. We estimate a time-calibrated phylogeny for 390 ranid species and use this phylogeny to analyze patterns of biogeography and diversification rates. As in hylids, we find a strong relationship between the timing of colonization of each region and its current diversity, with recent colonization of temperate regions from tropical regions. Diversification rates are similar in tropical and temperate clades, suggesting that neither accelerated tropical speciation rates nor greater temperate extinction rates explain high tropical diversity in this group. Instead, these results show the importance of historical biogeography in explaining high species richness in both the New World and Old World tropics.