Agitation leaching is a promising technology in hydrometallurgy for treating copper–cobalt oxide ores. In this work, the behavior of oxide ores containing around 2.3% Cu and 0.3% Co received from Congo was investigated for varying particle size, acidity, pulp density, temperature, leaching time, and reduction potential. XRD, optical microscopy (OM), and ICP-OES methods were used to examine the chemical composition, morphology, and metal content of the samples. The copper and cobalt recovery reached 88.2% and 82.5%, respectively, at room temperature, with a leaching time of 4 h, a pulp density of 33%, an acidity of 178 g/L, and no reductant. The Cu and Co remaining in the leaching residue were found to be in their sulfide forms and coated with dense and fine calcium sulfate. To improve the metal recovery, a combination of flotation and agitation leaching of the flotation tailings method was adopted, after which the Cu and Co recovery reached 96.6% and 86.0%, respectively.