Copper slags produced in vast quantities in smelting operations could be considered as secondary material sources instead of stockpiling them in landfills. This study investigates the recovery of valuable metals from copper slag and the valorisation of the leach residue as construction material in line with the principles of a circular economy. By taking into account that the environmental characterization of the as-received copper slag did not allow its disposal in landfills without prior treatment, chemical and biological leaching were tested for the recovery of metals. Pre-treatment with acids, namely HNO₃ and H₂SO₄, resulted in the extraction of several target metals and the production of an almost inert waste. Despite the clearly better oxidative conditions prevailing in the bioleaching reactors, chemical leaching resulted in the higher dissolution of Cu (71% vs. 51%), Co (70% vs. 36%), and Zn (65% vs. 44%). The acid consumption was much lower during the bioleaching experiments compared to the chemical leaching. The bioleach residue was suitable for its use as supplementary cementitious material, showing a better performance than the reference sample without causing any detrimental effects to the calcium aluminate cement (CAC) quality. The complete valorisation of copper slags is expected to improve the economics of the process, by avoiding landfill costs and producing saleable products with high added value.