Aggregates derived from waste, due to the growing awareness of global warming, are more and more often used in the concrete production process. This way, their disposal not only reduces the pollution of the Earth but also lowers the consumption of natural aggregates, which are limited. One of the new “eco” aggregates may be a ferronickel slag waste (FNSW), which was generated in post-war metallurgical processes and stored in Szklary (Lower Silesian, Poland). In order to determine the possibility of using ferronickel slag waste aggregate (FNSWA) in the concrete production process, new concrete mixtures were designed and tested. Physical properties (cone slump, air content, pH, and density), mechanical properties (compressive strength, flexural strength, and tensile strength), and thermal properties (thermal conductivity) were assessed for all new laboratory recipes. Moreover, the modulus of elasticity and Poisson’s ratio were determined. This study includes five different contents of FNSWA in the amount of 5%, 10%, 15%, 20%, and 25% of the mass of natural aggregate as its partial substitute. The final results were compared to the base sample (BS) containing 100% natural aggregate, which was granite.