It is a well-known fact that, ordinary Portland cement (OPC) is a major producer of CO2 and that has a negative impact to our environment. So, alternative cementing materials are of great research interest these days. In Ethiopia due to the downturn in economic conditions, the OPC price has shoot up that has become difficult to be afforded by common man and construction industries are struggling big time. On the other hand, Biomedical Waste Ash (BMWA) and Textile Sludge (TS) ash are plentily available in Ethiopia and disposal of these wastes have become a big concern for its production industries. So, in this research, an attempt has been made to check the viability of using these two wastes as cementing material in concrete as a partial replacement of OPC. C-40 concrete grade has been chosen for this experimental investigation. First, the physical and chemical properties of BMWA and TS were investigated. Further, several concrete mixes were produced with different percentages of these wastes as cementing material. At the fresh state of concrete, workability and density of the concrete were examined. Upon completion of curing of 28 days, the concrete mixes were tested for their mechanical and durability properties. From mechanical properties perspective, compressive strength, tensile strength and flexural strength tests were conducted. From durability point of view, water absorption and the effects of elevated temperature were studied. Finally, the microstructural studies were conducted by SEM and XRD to understand how these wastes influence the physical properties of concrete. The experimental results revealed that, use of BMWA and TS as partial replacement of cement in concrete enhances the mechanical and durability properties of concrete due to their pozzolanic properties. Hence, use of biomedical waste ash and textile sludge can definitely be considered a sustainable cementing material for the Ethiopian construction industry.