Extrapolation of band-limited signals in noisy conditions is an ill-posed least-squares estimation problem. To stabilize the extrapolation, derivative smoothness of signals to be extrapolated is introduced to a weighted-least-squares error criterion as prior information. One can adjust the weighting of the smoothness by employing multiple regularization parameters to be determined optimally. The extrapolated signal is given by using the generalized singular value decomposition, which is modified by the regularization. On the basis of a Bayesian statistical approach, a new information-theoretic criterion is presented to determined the optimal regularization parameters, which can give optimal balance between the smoothness prior and the observed signal data to attain stabilized extrapolation by optimal regularization.