This study aimed to tailor candelilla wax (CLW)‐based oleogels loaded with α‐tocopherol to mimic the rheological properties of conventional solid fats and enhance the nutritional value of food products. Desirability approach was utilized to optimize oleogels formulations based on rheological parameters of yield stress and gel‐to‐sol transition temperature of conventional solid fats (hydrogenated fat, butter, and margarine). Fat‐tailored oleogels were also characterized by their texture, thermal behavior, and microstructure. The concentration of CLW (0.75–4.0 wt%), but not of α‐tocopherol (0.5–10 wt%), affected the rheological behavior of oleogels. Yield stress and the gel‐to‐sol transition increased, respectively, from 2.00 to 200.8 Pa and from 40.2 to 64.8°C as the CLW concentration increased. α‐Tocopherol can be added to improve the nutritional value of CLW‐based oleogels without affecting their rheological fingerprint. The optimum formulations to mimic the rheological fingerprint of butter, margarine, and hydrogenated fat comprised CLW between 2.12 and 2.51 wt%, showing desirability values of 0.58, 0.76, and 0.73, respectively. Increasing the CLW contents increased the crystal number (4194 ± 381 to 7646 ± 544) and hardness (6.45 ± 0.30 to 10.4 ± 0.36 N) of fat‐tailored oleogels, besides accelerating crystallization. Therefore, it was possible to tailor oleogels structured with low CLW concentration (<2.5 wt%) loaded with α‐tocopherol to fairly replicate the rheological properties of margarine and hydrogenated fat. Butter‐like properties were achieved to a lesser extent. These oleogels might enhance the nutritional value of food products by incorporating the antioxidant vitamin E when used as substitutes for solid fat.