The objective of this study was to establish the most suitable mixtures of Tunisian illito-kaolinitic clay and industrial wastes (phosphogypsum [PG] and waste brick) to produce geopolymer binders. The raw clay sample was heated at 850 °C and characterized by chemical and thermal analyses, X-ray diffraction, and infrared spectroscopy. Four mixtures with different ratios (4%, 8%, 12%, and 16%) of PG as a partial replacement for the calcined clay were investigated. The obtained mixture powders were dissolved in a strong alkaline solution (10, 14, and 17 mol (NaOH)/L) and the produced geopolymers were preserved for 28 days and then characterized by determining their compressive strength. Results showed that increasing the percentage of PG up to 8% reveals an enhancement in the mechanical properties. The highest value of 36 MPa was attained for NaOH concentration of 14 M. At this optimal condition, the calcined clay was replaced by the powder of waste red brick and the produced geopolymer binders had almost the same mechanical property.