Purple acid phosphatases (PAPs) play a vital role in plant phosphorus nutrition, serving as a crucial family of metallo-phosphoesterase enzymes. This research aimed to identify the PAP genes from the A/B/D genomes of Triticum aestivum to elucidate evolutionary mechanisms of the gene family in plants and provide genomic information for subsequent research on phosphorous-use efficiency in wheat crops. In total, 105 PAP genes (TaPAPs) were identified from the A/B/D genomes by using the Arabidopsis thaliana and Oryza sativa PAP protein sequences as queries for BLASTP against the wheat protein database. The TaPAPs were grouped into six subfamilies, Ia (17), Ib (26), IIa (11), IIb (30), IIIa (12), and IIIb (9), based on their similarities in the structure of genes and the presence of conserved protein motifs. A majority of TaPAPs were derived from tandemly (20) or segmentally (87) duplicated, with the homoeologous chromosomes 5A/B/D harboring the most duplicated PAP genes. Further analysis indicated that TaPAPs were responsible for the modulation of seed, root, and leaf development and hormone synthesis and signaling, as well as plant responses to abiotic stresses, including low temperatures, drought, and anaerobic conditions. Nine TaPAPs (TaPAP9-4A/4B/4D, TaPAP24-6A/6B/6D, and TaPAP28-7A/7B/7D) were constitutively expressed in diverse tissues such as root, shoot, leaf, spike, and seed, while the remaining genes exhibited tissue-specific expression patterns. Concerning the response to phosphate (Pi) deprivation, 57 TaPAPs were highly expressed in roots under Pi stress, including TaPAP31-4A, 4B, and 4D homeologs from the subfamily IIIb. A TaPAP31-4A transgene in A. thaliana promoted plant growth and development while increasing plant resistance to Pi-deficiency stress by enhancing the secretion of phosphatase. These discoveries provide a scientific foundation for comprehending the role of TaPAPs, offering valuable insights for identifying additional candidate genes and fostering the development of new wheat varieties with enhanced tolerance to low phosphorus conditions.