Anthocyanins are the most important polyphenolic substances contained in blackcurrant fruits. They are responsible for the various health benefits caused, in particular, by their high antioxidant activity. Anthocyanins derived from anthocyanidins cyanidin and delphinidin are typical for blackcurrant fruits, especially their rutinoside and glucoside forms. These four anthocyanins usually represent about 97–98% of total anthocyanins in blackcurrant fruits. In this study, we developed and validated a new HPLC-DAD method for rapid anthocyanin separation and determination in fifteen perspective blackcurrant cultivars (‘Ruben’, ‘Ben Lomond’, ‘Ben Conan’, ‘Ceres’, ‘Moravia’, ‘Ometa’, ‘Lota’, ‘Fokus’, ‘Tenah’, ‘Sejanec’, ‘Consort’, ‘Triton’, ‘Ben Hope’, ‘Ben Gairn’, and one gooseberry hybrid ‘Josta’). Eight of them were monitored throughout the three-year experiment. The most represented anthocyanins in all monitored blackcurrant cultivars were delphinidin-3-rutinoside (36.7–63.6%), cyanidin-3-rutinoside (26.4–40.6%), delphinidin-3-glucoside (6.1–17.9%), and cyanidin-3-glucoside (1.3–9.9%). The individual anthocyanin proportion (%) in each cultivar was specific, and a similar profile was verified in a three-year period for eight available cultivars. Total anthocyanin content expressed as a sum of four major anthocyanins present in blackcurrants was compared with values expressed as the equivalent of cyanidin-3-glucoside, as many authors do. We revealed an underestimation of about 20% with the latter method. Cultivars with the highest average total anthocyanin content were ‘Ben Gairn’ (294.38 mg/100 g), ‘Ceres’ (281.31 mg/100 g), and ‘Ometa’ (269.09 mg/100 g).