Trehalose-6-phosphate phosphatases genes (TPPs) are involved in the development and stress response of plants by regulating the biosynthesis of trehalose, though little is currently known about TPPs in common wheat (Triticum aestivum L.). In this study, we performed a genome-wide identification of the TPP gene family in common wheat, and identified a total of 31 TaTPP genes. These were subdivided into six subfamilies based on the phylogenetic relationships and the conservation of protein in six monocot and eudicot plants. The majority of TPP genes were represented by 2–3 wheat homoalleles (named TaTPPX_ZA, TaTPPX_ZB, or TaTPPX_ZD), where Z is the location on the wheat chromosome of the gene number (X). We also analyzed the chromosomal location, exon-intron structure, orthologous genes, and protein motifs of the TaTPPs. The RNA-seq data was used to perform an expression analysis, which found 26 TaTPP genes to be differentially expressed based on spatial and temporal characteristics, indicating they have varied functions in the growth and development of wheat. Additionally, we assessed how the promoter regulatory elements were organized and used qRT-PCR in the leaves to observe how they were expressed following ABA, salt, low tempreture, and drought stress treatments. All of these genes exhibited differential expression against one or more stress treatments. Furthermore, ectopic expression of TaTPP11 in Arabidopsis exhibited a phenotype that delayed plant development but did not affect seed morphology. TaTPPs could serve important roles in the development and stress response in wheat. These results provide a basis for subsequent research into the function of TaTPPs.