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 (also referred to as co-option or molecular domestication), a process whereby TEs, which persist by replicating in the genome, transform into novel host genes, and persist by conferring phenotypic benefits. In eukaryotes, TE exaptation has made possible major evolutionary innovations, including the vertebrate adaptive immune system and the mammalian placenta; 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 exapted TE (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, MUSTANG (MUG) and FAR-RED ELONGATED HYPOCOTYL3 (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. Our approach is not limited to plant genomes and would be informative to apply, for example, in mammals.