CRISPR–Cas systems illustrate how noncoding RNAs (ncRNA) can program immune functions by targeting foreign DNA for degradation. Intriguingly, a widespread family of defense-associated reverse transcriptases (DRTs) instead leverages noncoding RNAs to direct programmable DNA synthesis during antiviral defense. Here we investigate the mechanism of immunity mediated by tripartite DRT10 systems, which rely on a membrane effector protein and RT-catalyzed generation of repetitive DNA. The RT associates with a structured ncRNA and uses a short template region to catalyze protein-primed, processive synthesis of tandem DNA repeats. Repeat addition proceeds through iterative cycles of template-directed extension and realignment encoded within the ncRNA. This mechanism closely parallels the repeat-addition strategy of telomerase, revealing an unexpected connection between antiviral RT systems in bacteria and conserved pathways of repetitive DNA synthesis in eukaryotes that maintain genome integrity.