This paper presents a Bayesian fusion technique for multi-band images. The observed images are related to the high spectral and high spatial resolution image to be recovered through physical degradations, e.g., spatial and spectral blurring and/or subsampling defined by the sensor characteristics. The fusion problem is formulated within a Bayesian estimation framework. An appropriate prior distribution related to the linear mixing model for hyperspectral images is introduced. To compute Bayesian estimators of the scene of interest from its posterior distribution, a Gibbs sampling algorithm is proposed to generate samples asymptotically distributed according to the target distribution. To efficiently sample from this high-dimensional distribution, a Hamiltonian Monte Carlo step is introduced in this Gibbs sampler. The efficiency of the proposed fusion method is evaluated with respect to several state-of-the-art fusion techniques.