Tyrosinase is the central enzyme involved in the highly complex process of melanin formation, catalyzing the rate-limiting steps of this biosynthetic pathway. Due to such a preponderant role, it has become a major target in the treatment of undesired skin pigmentation conditions and also in the prevention of enzymatic food browning. Numerous phenolic-based structures from natural sources have been pointed out as potential tyrosinase inhibitors, including anthocyanins. The aim of the present study was to individually assess the tyrosinase inhibitory activity of eight purified compounds with a variable degree of structural complexity: native anthocyanins, deoxyanthocyanins, and pyranoanthocyanins. The latter two, the groups of anthocyanin-related compounds with enhanced stability, were tested for the first time. Compounds 1 to 4 (luteolinidin, deoxymalvidin, cyanidin-, and malvidin-3-O-glucoside) revealed to be the most effective inhibitors, and further kinetic studies suggested their inhibition mechanism to be of a competitive nature. Structure–activity relationships were proposed based on molecular docking studies conducted with mushroom tyrosinase (mTYR) and human tyrosinase-related protein 1 (hTYRP1) crystal structures, providing information about the binding affinity and the different types of interactions established with the enzyme’s active center which corroborated the findings of the inhibition and kinetic studies. Overall, these results support the applicability of these compounds as pigmentation modulators.