In the estimation of spatiotemporal slip models, kinematic source inversions using Akaike's Bayesian Information Criterion (ABIC) and the multiple-time-window method have often been used. However, there are cases in which conventional ABIC-based source inversions do not work well in the determination of hyperparameters when a non-negative slip constraint is used. In order to overcome this problem, a new source inversion method was developed in this study. The new method introduces a fully Bayesian method into the kinematic multiple-time-window source inversion. The multiple-time-window method is one common way of parametrizing a source time function and is highly flexible in terms of the shape of the source time function. The probability distributions of model parameters and hyperparameters can be directly obtained by using the Markov chain Monte Carlo method. These probability distributions are useful for simply evaluating the uniqueness and reliability of the derived model, which is another advantage of a fully Bayesian method. This newly developed source inversion method was applied to the 2011 Ibaraki-oki, Japan, earthquake (M-w 7.9) to demonstrate its usefulness. It was demonstrated that the problem with using the conventional ABIC-based source inversion method for hyperparameter determination appeared in the spatiotemporal source inversion of this event and that the newly developed source inversion could overcome this problem.