Amyloid fibrils are homo-molecular protein polymers that play an important role in disease and biological function. While much is known about their kinetics and mechanisms of formation, the origin and magnitude of their thermodynamic stability has received significantly less attention. This is despite the fact that the thermodynamic stability of amyloid fibrils is an important determinant of their lifetimes and processing in vivo. Here we use depolymerization by chemical denaturants of amyloid fibrils of two different proteins (PI3K-SH3 and glucagon) at different concentrations and show that the previously applied isodesmic linear polymerization model is an oversimplification that does not capture the concentration dependence of chemical depolymerization of amyloid fibrils. We show that cooperative polymerization, which is compatible with the picture of amyloid formation as a nucleated polymerization process, is able to quantitatively describe the thermodynamic data. We use this combined experimental and conceptual framework in order to probe the ionic strength dependence of amyloid fibril stability. In combination with previously published data on the ionic strength dependence of amyloid fibril growth kinetics, our results provide strong evidence for the product-like nature of the transition state of amyloid fibril growth.