The nuclear factor Y (NF-Y) family is comprised of transcription factors that have been implicated in multiple plant biological processes. However, little is known about this family in potato. In the present study, a total of 41 StNF-Y genes were identified in the potato genome. In addition, the phylogenetic, gene structure, motif, and chromosomal location of this family were analyzed. The tissue expression profiles based on RNA-seq data showed that 27 StNF-Y genes had tissue-specific expression, while the remaining 14 had low expression in all tissues. Publicly available transcriptomics data from various abiotic stresses revealed several stress-responsive StNF-Y genes, which were further verified via quantitative real-time polymerase chain reaction experiments. Furthermore, the StNF-YC9 gene was highly induced by dehydration and drought treatments. StNF-YC9 protein was mainly localized in the nucleus and cytoplasmic membrane. Overexpressing StNF-YC9 potato lines (OxStNF-YC9) had significantly increased in root length and exhibited stronger stomatal closure in potato treated by polyethylene-glycol and abscisic acid. In addition, OxStNF-YC9 lines had higher photosynthetic rates and decreased water loss under short-term drought stress compared to wild-type plants. During long-term drought stress, OxStNF-YC9 lines had higher proline levels, lower malondialdehyde content, and increased activity of several antioxidant enzymes, including superoxide dismutase, catalase, and peroxidase. This study increased our understanding of the StNF-Y gene and suggested that StNF-YC9 played an important role in drought tolerance by increased the photosynthesis rate, antioxidant enzyme activity, and proline accumulation coupled to lowered malondialdehyde accumulation in potato.