Once perceived as merely selfish, transposable elements (TEs) are now recognized as potent agents of adaptation. One way TEs contribute to evolution is through TE exaptation, a process whereby TEs, which persist by replicating in the genome, transform into novel host genes, which persist by conferring phenotypic benefits. Known exapted TEs (ETEs) contribute diverse and vital functions, and may facilitate punctuated equilibrium, yet little is known about this process. To better understand TE exaptation, we designed an approach to resolve the phylogenetic context and timing of exaptation events and subsequent patterns of ETE diversification. Starting with known ETEs, we search in diverse genomes for basal ETEs and closely related TEs, carefully curate the numerous candidate sequences, and infer detailed phylogenies. To distinguish TEs from ETEs, we also weigh several key genomic characteristics including repetitiveness, terminal repeats, pseudogenic features, and conserved domains. Applying this approach to the well-characterized plant ETEs MUG and FHY3, we show that each group is paraphyletic and we argue that this pattern demonstrates that each originated in not one but multiple exaptation events. These exaptations and subsequent ETE diversification occurred throughout angiosperm evolution including the crown group expansion, the angiosperm radiation, and the primitive evolution of angiosperms. In addition, we detect evidence of several putative novel ETE families. Our findings support the hypothesis that TE exaptation generates novel genes more frequently than is currently thought, often coinciding with key periods of evolution.