We test the recently proposed history-augmented Solow model with respect to its predictions on the evolution of cross-country income inequality between nowadays industrialized countries. Using a broad range of deterministic and stochastic simulations, we illustrate that the model predicts the following pattern. There is low cross-country income inequality before the Industrial Revolution (during the period of “Malthusian Stagnation”), strongly increasing cross-country income inequality afterwards (the period of “The Great Divergence”), and finally declining cross-country income inequality toward a level that is higher than the level before the Industrial Revolution (the period of “Club Convergence”). Tests on the structural break of the observable time series of income dispersion and segmented regressions show that this development is fully consistent with the empirical evolution of cross-country income inequality since the late 19th century. Additional tests using quadratic polynomials, fractional polynomials, polynomial ridge regressions, and polynomial LASSO regressions confirm this finding.