RNA polymers are synthesized, degraded, and modified through several varied cellular processes. The ability of cells to degrade and recycle their RNA products is a ubiquitous and essential function. Specific subsets of endo- and exoribonucleases catalyze the reactions that ultimately replenish the pool of mono-ribonucleotides. While exoribonucleases largely share overlapping substrates and functions, nanoRNases are unique in that they alone degrade short RNA fragments in a process that is essential for cellular fitness. Oligoribonuclease (Orn) was the first nanoRNase characterized and described for its essentiality in many bacteria, however, the basis of its substrate preference remained unclear. Here we elaborate on Orn’s unique function and show that it exhibits exquisite preference for diribonucleotides. Crystal structures of substrate-bound Orn reveal a narrowly constrained active site optimized for diribonucleotides with 5’-monophosphates, with structural features that impart conformational restrictions on bound substrates. While other cellular RNases process RNA polymers down to diribonucleotides, Orn is the only diribonucleotidase in Pseudomonas aeruginosa, preventing the toxic accumulation of diribonucleotides. In addition to completing the terminal step of RNA degradation, Orn was previously shown to catalyze the final step in cyclic di-GMP degradation in P. aeruginosa, cleaving the intermediate linear di-GMP to GMP. As a specific diribonucleotidase, Orn resides at the confluence of RNA metabolism and bacterial second messenger signaling. While Orn is conserved from bacteria to humans, it is not ubiquitous in all organisms, or even all bacteria with machinery for cyclic dinucleotide signaling. Given the critical role of diribonucleotide degradation in general cell fitness, we asked whether such specific activity exists in organisms lacking Orn-type exoribonucleases. Through quantitative structure-function analyses we show here that NrnC-type nanoRNases share this narrow substrate preference with Orn. Although NrnC employs similar structural features that distinguish these two classes as diribonucleotidases from other exoribonucleases, these key determinants for diribonucleotidase activity are realized through distinct structural scaffolds. The structures together with comparative genomic analyses of the phylogeny of DEDD-type exoribonucleases implicate convergent evolution in the separate emergence of diribonucleotidase activity in various organisms. The evolutionary pressure to maintain diribonucleotidase activity further underlines the important function of these analogous proteins.