The present invention is a new and distinct thornless blackberry cultivar named ‘Black Jack’, which is capable of producing large and firm fruit with high soluble solids. The cultivar is characterized by its thornlessness and its fruit attributes. It has the fruit morphology of other very large blackberries grown on thorny cultivars, namely uneven drupelets. It is, however, firmer than other large fruited types, and has very high soluble solids, up to 14%. ‘Black Jack’ plants are also unusual amongst the very large blackberry cultivars in that they produce commercial quantities of fruit, greater than 13 tons per acre on 2 year old potted plants.