The studies on the determination of the characteristics of the amyloid fibril interaction with the dye were based on the analysis of the dependence of the ThT fluorescence intensity on its concentration in the solution containing the amyloid fibrils. In the present work, we revealed that this intuitive approach provided erroneous data. We propose a new approach which provides a means for characterizing the interaction of thioflavin T (ThT) with amyloid fibrils and for determining the binding stoichiometry and binding constants, absorption spectrum, molar extinction coefficient, and fluorescence quantum yield of the ThT bound to the sites of different binding modes of fibrils. The key point of this approach is sample preparation by equilibrium microdialysis. The efficiency of the proposed approach is demonstrated via the examination of the ThT binding to insulin and Aβ42 fibrils as well as to the native form of the Electrophorus electricus acetylcholinesterase. We show that the peculiarities of ThT interaction with amyloid fibrils depend on the amyloidogenic protein and on the binding mode. This approach is universal and can be used for the analysis of binding mechanism of any dye that interacts with its receptor. Therefore, the proposed approach represents an important addition to the existing arsenal of means for the diagnostics and therapy of the neurodegenerative diseases.