Multispectral and hyperspectral data fusion allows the restoration of data with increased spatial and spectral resolutions. A common approach is to solve an ill-posed inverse problem by minimizing a regularized least squares criterion. This minimization usually requires an iterative gradient-based method, but this paper demonstrates the existence of an explicit solution. Direct models of the imager and the spectrometer are described, the explicit solution is developed, and an application on simulated data from the James Webb Space Telescope is presented. A potential time saving of a factor of 1 000 is highlighted by the proposed method.