As a crop irrigated primarily by rain, the quality and yield of peanuts are significantly limited by drought. To date, many studies have indicated that fatty acid desaturase (FAD) genes enhance plant tolerance to drought stresses. In this study, 16, 15, and 31 FADs were identified in Arachis duranensis, Arachis ipaensis, and Arachis hypogaea, respectively. All the FADs were divided into four subfamilies, which had relatively conserved gene structures, motifs, and domains. The synteny relationships and chromosomal position analysis showed that the FADs in subgenome pairs, A. duranensis-A. hypogaea (AA) and A. ipaensis-A. hypogaea (BB), were homologous, and their physical locations were consistent. The Ka/Ks results indicated that nine FAD genes underwent a purifying selection, and Ah|FAD3.2 experienced positive selection during tetraploid peanut speciation. Various cis-acting elements related to hormone signaling and stress responsiveness in promoters and the predicted miRNA targeting Ah|FADs suggested that these genes play crucial roles in drought tolerance. The expression profiles of Ah|FADs in 22 tissues and drought-tolerant and -sensitive cultivars under drought stress suggested that 4 and 6 FADs were putative genes related to oil accumulation and drought, respectively. These findings will help provide insight into the potential functional roles of the FAD genes, which may aid in dealing with plant drought stress.