Nuclear factor-Y (NF-Y) transcription factors are heterotrimeric complexes that are widely distributed in eukaryotes and play essential roles in many biological processes. Although NF-YA proteins have been characterized in numerous plants, their contribution to the response of durum wheat (Triticum turgidum ssp. durum) to environmental factors has not been reported. Thus, this study was aimed at identification and characterization of Triticum turgidum TtNF-YA family members through genome-wide analysis. Twelve NF-YA genes were discovered in Triticum turgidum. Discovered genes were distributed across eight chromosomes, while their encoded proteins were localized in cell nucleus. Structure and motif pattern analyses revealed that the TtNF-YA genes were relatively conserved. The expression of TtNF-YAs genes was significantly induced by several stressors and their expression profiles differed in various tissues and at various development stages. Notably, TtNF-YA2 A-1 and TtNF-YA2B-1 exhibited the greatest increase in response to Polyethylene glycol, while TtNF-YA4 A and TtNF-YA4B-1 showed the highest increase under salt stress. Additionally, TtNF-YA5B-1 and TtNF-YA6 A-1 displayed pronounced upregulation when exposed to exogenous Abscisic acid, suggesting that TtNF-YA are involved in a series of cellular and developmental events. This finding was corroborated by the recognition of several cis-regulatory elements in the TtNF-YAs promoter region, associated with the applied treatments. Overexpression of TtNF-YA2 A-1, TtNF-YA2B-1, TtNF-YA4 A, TtNF-YA4 A-1, TtNF-YA4B-1, and TtNF-YA5 A-2 genes in Saccharomyces cerevisiae showed that these genes increase cell tolerance to multiple stresses. Our results will facilitate subsequent functional analysis of TtNF-YAs genes, which emerge as promising targets for genetic engineering for increasing wheat tolerance to multiple stresses.