Grape seeds (GS) and grape skins (GK) are natural sources of polyphenols with antioxidant capacity. An experiment was conducted to investigate in chickens the effect of including GS and GK (40 g/kg), individually or combined in different proportions (20 g/kg GS–20 g/kg GK; 30 g/kg GS–10 g/kg GK; 10 g/kg GS–30 g/kg GK), in a corn-soybean diet on growth performance, ileal and excreta contents of total extractable polyphenols (TEP) and tannins, ileal digestibility of protein, plasma and meat α-tocopherol concentration and lipid oxidation (assessed by measuring the thiobarbituric acid reactive substances, TBARS) of stored thigh meat. Neither growth performance parameters nor ileal digestibility of protein were affected by dietary treatments. As compared with control birds, chickens fed the grape byproduct diets showed higher ileal (p < 0.001) and excreta (p < 0.001) TEP and tannins contents. Dietary inclusion of grape byproducts increased α-tocopherol concentration both in plasma (p < 0.001) and in thigh meat (p < 0.01 at 1 d; p < 0.001 at 7 d), as compared with the control group. The highest plasma α-tocopherol concentrations were reached with the 30 g/kg GS–10 g/kg GK and 20 g/kg GS–20 g/kg GK combinations. On day 1 of meat storage, no differences on meat α-tocopherol concentration were found among the grape byproducts treatments but on day 7 of storage, the 20 g/kg GS–20 g/kg GK and 10 g/kg GS–30 g/kg GK combinations led to the highest α-tocopherol concentrations in chicken thigh meat. After seven days of refrigerated storage of meat, the TBARS value was lower in chickens fed the grape byproducts diets than in control birds (1.27 vs. 2.49 mg MDA/kg, p < 0.001). Moreover, among the different grape byproduct treatments, the lowest MDA values were reached with the diets containing GK at rates from 20 to 40 g/kg. In conclusion, dietary incorporation of 40 g/kg of GS and GK added separately or combined increased the plasma and meat α-tocopherol content. Furthermore, the combinations of GS and GK with a proportion of GK of at least 50% optimised α-tocopherol concentration both in plasma and in thigh meat and mitigated lipid oxidation in 7-day stored meat.