Large amounts of yoghurt acid whey (YAW) are annually generated as a result of Greek-style yoghurt production, which poses a great hazard to the environment. In terms of sustainability, YAW application in the meat industry appears as a great alternative since meat marination with natural solutions is a practice that continuously gains ground due to its positive effects on meat sensory attributes. The aim of the present study was to determine the quality characteristics and oxidative status of pork and chicken meat after their marination in yoghurt acid whey. Forty samples per meat type were randomly assigned into five groups: CON, without YAW marination; YAW1 and YAW3, in which meat was marinated at 4 °C and a pH of 4.5 for 15 and 10 h, respectively; or YAW2 and YAW4, in which meat was handled as in the YAW1 and YAW3 group, respectively, while hesperidin at 2 g/L was also incorporated into the marinade. As shown, meat shear force values were decreased in pork but not in chicken meat samples. Meat pH values were also generally decreased, while lightness was increased in raw but not in cooked meat samples as an effect of marination. Moreover, meat oxidative stability was improved to a greater extent in chicken than in pork meat. In order to find the ideal marination period for pork meat, we further immersed it into YAW for 5 h. However, this treatment affected neither meat tenderness and the other quality properties nor meat oxidation rates. In general, hesperidin addition did not have an additional or side effect on the quality traits of pork and chicken meat. As it can be concluded, pork meat marination in YAW for 10–15 h improves tenderness, but 5 h of marination does not. On the other hand, the tenderness of chicken meat was not affected, but its oxidative stability was greatly improved after remaining in the YAW marinade for 10–15 h.