In this article, we derive closed-form expressions of fractional moment-based estimators for the Gamma-Gamma fading channel parameters. Most notably, as a special case of the closed-form expressions, the optimal moment-based estimators are derived by using not only the moments of the signal power but also the moments of its logarithm and their joint moments. The performance of the derived optimal moment-based estimators is analyzed in terms of the normalized mean square error via Monte Carlo simulations, along with that of conventional moment-based estimators, maximum-likelihood estimators, and Cramér-Rao lower bounds. From the numerical results, we show that the optimal moment-based estimators are superior to the conventional moment-based estimators and achieve near maximum-likelihood estimators and Cramér-Rao lower bounds performance under various channel conditions.