Ty3/Gypsy long terminals repeat (LTR) retrotransposons are structurally and phylogenetically close to retroviruses. Two notable structural differences between these groups of genetic elements are 1) the presence in retroviruses of an additional envelope gene, env, which mediates infection, and 2) a specific dual ribonuclease H (RNH) domain encoded by the retroviral pol gene. However, similar to retroviruses, many Ty3/Gypsy LTR retrotransposons harbor additional env-like genes, promoting concepts of the infective mode of these retrotransposons. Here, we provide a further line of evidence of similarity between retroviruses and some Ty3/Gypsy LTR retrotransposons. We identify that, together with their additional genes, plant Ty3/Gypsy LTR retrotransposons of the Tat group have a second RNH, as do retroviruses. Most importantly, we show that the resulting dual RNHs of Tat LTR retrotransposons and retroviruses emerged independently, providing strong evidence for their convergent evolution. The convergent resemblance of Tat LTR retrotransposons and retroviruses may indicate similar selection pressures acting on these diverse groups of elements and reveal potential evolutionary constraints on their structure. We speculate that dual RNH is required to accelerate retrotransposon evolution through increased rates of strand transfer events and subsequent recombination events.