Total Variation (TV) based regularization has been widely applied in restoration problems due to its simple derivative filters based formulation and robust performance. While first order TV suffers from staircase effect, second order TV promotes piece-wise linear reconstructions. Generalized Multi-Order Total Variation (GMO-TV) is proposed as a novel regularization method which incorporates a new multivariate Laplacian prior on signal derivatives in a non-quadratic regularization functional, that utilizes subtle inter-relationship between multiple order derivatives. We also propose a computational framework to automatically determine the weight parameters associated with these derivative orders, rather than treating them as user parameters. Using simulation results on ECG and EEG signals, we show that GMO-TV performs better than related regularization functionals.