The search for more sustainable construction materials, capable of complying with quality standards and current innovation policies, aimed at saving natural resources and reducing global pollution, is one of the greatest present societal challenges. In this study, an innovative recycled aggregate concrete (RAC) is designed and produced based on the use of a coarse recycled aggregate (CRA) crushing concrete with electric arc furnace slags as aggregate. These slags are a by-product of the steelmaking industry and their use, which avoids the use of natural aggregates, is a new trend in concrete and pavement technology. This paper has investigated the effects of incorporating this type of CRA in concrete at several replacement levels (0%, 20%, 50% and 100% by volume), by means of the physical, mechanical and durability characterization of the mixes. The analysis of the results has allowed the benefits and disadvantages of these new CRAs to be established, by comparing them with those of a natural aggregate concrete (NAC) mix (with 0% CRA incorporation) and with the data available in the literature for concrete made with more common CRA based on construction and demolition waste (CDW). Compared to NAC, similar compressive strength and tensile strength values for all replacement ratios have been obtained. The modulus of elasticity, the resistance to chloride penetration and the resistance to carbonation are less affected by these CRA than when CRA from CDW waste is used. Slight increases in bulk density over 7% were observed for total replacement. Overall, functionally good mechanical and durability properties have been obtained.