Auxin response factors (ARFs) are important transcription factors involved in both the auxin signaling pathway and the regulatory development of various plant organs. In this study, 23 TaARF members encoded by a total of 68 homeoalleles were isolated from 18 wheat chromosomes (excluding chromosome 4). The TaARFs, including their conserved domains, exon/intron structures, related microRNAs, and alternative splicing (AS) variants, were then characterized. Phylogenetic analysis revealed that members of the TaARF family share close homology with ARFs in other grass species. qRT-PCR analyses revealed that 20 TaARF members were expressed in different organs and tissues and that the expression of some members significantly differed in the roots, stems, and leaves of wheat seedlings in response to exogenous auxin treatment. Moreover, protein network analyses and co-expression results showed that TaTIR1-TaARF15/18/19-TaIAA13 may interact at both the protein and genetic levels. The results of subsequent evolutionary analyses showed that three transcripts of TaARF15 in the A subgenome of wheat exhibited high evolutionary rate and underwent positive selection. Transgenic analyses indicated that TaARF15-A.1 promoted the growth of roots and leaves of Arabidopsis thaliana and was upregulated in the overexpression plants after auxin treatment. Our results will provide reference information for subsequent research and utilization of the TaARF gene family.