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Asbestos tailings represent a historical liability in many countries. Canada aims at transforming this industrial legacy into an opportunity to both mitigate the environmental footprint and recover critical (such as magnesium, nickel, chromium, and cobalt) and strategic metals, which represent significant economic development potential. This study aimed to investigate the recovery of critical and strategic metals (CSMs) from asbestos tailings using hydrochloric (HCl) acid leaching, with acid concentration (2–12 mol/L), leaching temperature (20–90 °C), and solid–liquid ratio (10–40%) as key process parameters. The tailing samples studied is composed mostly of chrysotile and lizardite. It contains about 40% magnesium (as its oxide MgO) and nickel and chromium showing contents 52 and 60 times higher than their respective average crustal abundances (Clarke values). Iron content is 8.7% (expressed as its ferric oxide Fe2O3). To optimize key factors influencing the leaching process, a statistical experimental design was employed. The designed leaching experiments were subsequently performed, and results were used to define leaching conditions aiming at maximizing Mg and Ni recoveries while minimizing iron contamination using response surface methodology (RSM) based on the central composite design (CCD). A quadratic polynomial model was developed to describe the relationship between the process parameters and metal recoveries. Among the tested effects of acid concentration, temperature, and pulp density on magnesium recovery, the modeling indicated that both hydrochloric acid concentration and leaching temperature significantly enhanced metal recovery, whereas increasing pulp density had a negative effect at low temperature. The empirical mathematical model derived from the experimental data, accounting for the uncertainties on chemical data, indicated that high magnesium recovery was achieved at 90 °C, with 10–12 N hydrochloric acid and a solid-to-liquid ratio of 33.6–40%. These findings reveal the potential for the recovery of critical and strategic metals, both in terms of efficiency and economic viability.