The aim of this study was to assess the effects of dietary anthocyanin addition on volatile compounds of meat from goat kids during ageing. For this work, 60 male and female kids were divided into two groups: red orange and lemon extract (RLE group; n = 30), which received an RLE extract (90 mg/kg of live weight); and control (CON group; n = 30). The phytoextract in dry powder form was rich in bioflavonoids such as flavanones (about 16%) and anthocyanins (about 3%). After slaughtering, the longissimus thoracis et lumborum muscle was aged at 4 °C. The volatile organic compound (VOC) and sensorial analyses were carried out at 1, 3 and 7 days. A total of 10 chemical families were identified during the ageing process. Aldehydes were the most abundant VOC, followed by ketones and alcohols. Their contents increased during the process, showing after 7 days of ageing mean values of 20,498, 2193 and 1879 ng/g of meat, respectively. Regarding dietary effects, carboxylic acids, hydrocarbons and thiols presented significant differences between treatments, with higher carboxylic acid contents observed in RLE samples (437 vs. 467 ng/g of meat for CON and RLE batches, respectively; p < 0.05). On the contrary, hydrocarbons (436 vs. 254 ng/g of meat for CON and RLE batches, respectively) and thiols (160 vs. 103 ng/g of meat for CON and RLE batches, respectively) displayed significantly (p < 0.01) higher amounts in CON compared to the RLE group. Regarding ageing time, the tenderness, juiciness, odour and overall assessment parameters showed significantly higher scores at the end of the whole process (p < 0.05). On the other hand, only odour displayed significant differences between treatments, reaching higher scores in CON samples (p < 0.05). Therefore, ageing time improved the sensorial properties (tenderness, juiciness, odour and overall assessment) and the VOC content, whereas the inclusion of anthocyanins in the kids’ diet did not have a great impact on the properties of aged meat.