Abstract Killer lymphocyte granzyme (Gzm) serine proteases induce apoptosis of pathogen-infected cells and tumor cells. Many known Gzm substrates are nucleic acid binding proteins, and the Gzms accumulate in the target cell nucleus by an unknown mechanism. In this study, we show that human Gzms bind to DNA and RNA with nanomolar affinity. Gzms cleave their substrates most efficiently when both are bound to nucleic acids. RNase treatment of cell lysates reduces Gzm cleavage of RNA binding protein targets, whereas adding RNA to recombinant RNA binding protein substrates increases in vitro cleavage. Binding to nucleic acids also influences Gzm trafficking within target cells. Preincubation with competitor DNA and DNase treatment both reduce Gzm nuclear localization. The Gzms are closely related to neutrophil proteases, including neutrophil elastase (NE) and cathepsin G. During neutrophil activation, NE translocates to the nucleus to initiate DNA extrusion into neutrophil extracellular traps, which bind NE and cathepsin G. These myeloid cell proteases, but not digestive serine proteases, also bind DNA strongly and localize to nuclei and neutrophil extracellular traps in a DNA-dependent manner. Thus, high-affinity nucleic acid binding is a conserved and functionally important property specific to leukocyte serine proteases. Furthermore, nucleic acid binding provides an elegant and simple mechanism to confer specificity of these proteases for cleavage of nucleic acid binding protein substrates that play essential roles in cellular gene expression and cell proliferation.