Effective maintenance of plant iron (Fe) homoeostasis relies on a network of transcription factors (TFs) that respond to environmental conditions and regulate Fe uptake, translocation, and storage. The iron-related transcription factor 3 (IRO3), as well as haemerythrin motif-containing really interesting new gene (RING) protein and zinc finger protein (HRZ), are major regulators of Fe homeostasis in diploid species like Arabidopsis (Arabidopsis thaliana) and rice (Oryza sativa L.), but remain uncharacterised in hexaploid bread wheat (Triticum aestivum L.). In this study, we have identified, annotated, and characterised three TaIRO3 homoeologs and six TaHRZ1 and TaHRZ2 homoeologs in the bread wheat genome. Protein analysis revealed that TaIRO3 and TaHRZ proteins contain functionally conserved domains for DNA-binding, dimerisation, Fe binding, or polyubiquitination, and phylogenetic analysis revealed clustering of TaIRO3 and TaHRZ proteins with other monocot IRO3 and HRZ proteins, respectively. Quantitative reverse-transcription PCR analysis revealed that all TaIRO3 and TaHRZ homoeologs have unique tissue expression profiles and are upregulated in shoot tissues in response to Fe deficiency. After 24 h of Fe deficiency, the expression of TaHRZ homoeologs was upregulated, while the expression of TaIRO3 homoeologs was unchanged, suggesting that TaHRZ functions upstream of TaIRO3 in the wheat Fe homeostasis TF network.