Transposable elements amplify in genomes as selfish DNA elements and challenge host fitness because their intrinsic integration steps during mobilization can compromise genome integrity. In gene-dense genomes, transposable elements are notably under selection to avoid insertional mutagenesis of host protein-coding genes. We describe an example of convergent evolution in the distantly related amoebozoan Dictyostelium discoideum and the yeast Saccharomyces cerevisiae, in which the D. discoideum retrotransposon DGLT-A and the yeast Ty3 element developed different mechanisms to facilitate position-specific integration at similar sites upstream of tRNA genes. Transcription of tRNA genes by RNA polymerase III requires the transcription factor complexes TFIIIB and TFIIIC. Whereas Ty3 recognizes tRNA genes mainly through interactions of its integrase with TFIIIB subunits, the DGLT-A-encoded ribonuclease H contacts TFIIIC subunit Tfc4 at an interface that covers tetratricopeptide repeats (TPRs) 7 and 8. A major function of this interface is to connect TFIIIC subcomplexes τA and τB and to facilitate TFIIIB assembly. During the initiation of tRNA gene transcription τB is displaced from τA, which transiently exposes the TPR 7/8 surface of Tfc4 on τA. We propose that the DGLT-A intasome uses this binding site to obtain access to genomic DNA for integration during tRNA gene transcription.