This article demonstrates the possibility of producing alkali-activated hybrid cements based on fly ash (FA), and construction and demolition wastes (concrete waste, COW; ceramic waste, CEW; and masonry waste, MAW) using sodium sulfate (Na2SO4) (2–6%) and sodium carbonate (Na2CO3) (5–10%) as activators. From a mixture of COW, CEW, and MAW in equal proportions (33.33%), a new precursor called CDW was generated. The precursors were mixed with ordinary Portland cement (OPC) (10–30%). Curing of the materials was performed at room temperature (25 °C). The hybrid cements activated with Na2SO4 reached compressive strengths of up to 31 MPa at 28 days of curing, and the hybrid cements activated with Na2CO3 yielded compressive strengths of up to 22 MPa. Based on their mechanical performance, the optimal mixtures were selected: FA/30OPC-4%Na2SO4, CDW/30OPC-4%Na2SO4, FA/30OPC-10%Na2CO3, and CDW/30OPC-10%Na2CO3. At prolonged ages (180 days), these mixtures reached compressive strength values similar to those reported for pastes based on 100% OPC. A notable advantage is the reduction of the heat of the reaction, which can be reduced by up to 10 times relative to that reported for the hydration of Portland cement. These results show the feasibility of manufacturing alkaline-activated hybrid cements using alternative activators with a lower environmental impact.