A systematic study on the formation and stability of the icosahedral quasicrystalline (IQC) Al70Cu20Fe10 alloy has been carried out using electrothermal explosion (ETE) reaction as a preparation method. The influence of added elements on the formation of icosahedral phase has been investigated by Mossbauer spectroscopy, XRD, and field emission scanning electron microscopy (FESEM). Combined ball milling and ETE reaction (BM-ETE) of Al63Cu25Fe12 composition resulted in the formation of the ICQ Fe10Cu20Al70 phase with a face-centered structure. In all cases, an Al(Cu, Fe) solid solution and β-Fe3Al have been detected along with the ICQ phase. The icosahedral phase appears to form in a peritectoid-type reaction between Fe3Al and Al2Cu. A mechanism for formation of the IQC phase in the Al-Cu-Fe system was suggested. VSM measurements showed the ferromagnetic behavior of the alloy. The Mossbauer measurements in transmission and XRD data showed that the reaction product contained 65% Fe10Cu20Al70 with an admixture of β-Fe3Al and Al2Cu.