Image fusion is a valuable framework which combines two or more images of the same scene from one or multiple sensors, allowing to improve the resolution of the images and increase the interpretable content. In remote sensing a common fusion problem consists of merging hyperspectral (HS) and multispectral (MS) images that involve large amount of redundant data, which ignores the highly correlated structure of the datacube along the spatial and spectral dimensions. Compressive HS and MS systems compress the spectral data in the acquisition step allowing to reduce the data redundancy by using different sampling patterns. This work presents a compressed HS and MS image fusion approach, which uses a high dimensional joint sparse model. The joint sparse model is formulated by combining HS and MS compressive acquisition models. The high spectral and spatial resolution image is reconstructed by using sparse optimization algorithms. Different fusion spectral image scenarios are used to explore the performance of the proposed scheme. Several simulations with synthetic and real datacubes show promising results as the reliable reconstruction of a high spectral and spatial resolution image can be achieved by using as few as just the 50% of the datacube.