Natural killer (NK) cells are innate lymphocytes that have features of adaptive immunity such as clonal expansion and generation of long-lived memory. Interleukin-12 (IL-12) signaling through its downstream transcription factor signal transducer and activator of transcription 4 (STAT4) is required for the generation of memory NK cells after expansion. We identify gene loci that are highly enriched for STAT4 binding using chromatin immunoprecipitation sequencing for STAT4 and the permissive histone mark H3K4me3 in activated NK cells. We found that promoter regions of Runx1 and Runx3 are targets of STAT4 and that STAT4 binding during NK cell activation induces epigenetic modifications of Runx gene loci resulting in increased expression. Furthermore, specific ablation of Runx1, Runx3, or their binding partner Cbfb in NK cells resulted in defective clonal expansion and memory formation during viral infection, with evidence for Runx1-mediated control of a cell cycle program. Thus, our study reveals a mechanism whereby STAT4-mediated epigenetic control of individual Runx transcription factors promotes the adaptive behavior of antiviral NK cells.