The on-board compression of remote sensed hyperspectral images is an important task nowadays. One of the main difficulties is that the compression of these images must be performed in the satellite which carries the hyperspectral sensor. Hence, this process must be performed by space qualified hardware, having area, power and speed limitations. Moreover, it is important to achieve high compression ratios without compromising the quality of the decompress image. In this manuscript we proposed a new methodology for compressing hyperspectral images based on hyperspectral image fusion concepts. The proposed compression process has two independent steps. The first one is to spatially degrade the remote sensed hyperspectral image to obtain a low resolution hyperspectral image. The second step is to spectrally degrade the remote sensed hyperspectral image to obtain a high resolution multispectral image. These two degraded images are then send to the earth surface, where they must be fused using a fusion algorithm for hyperspectral and multispectral image, in order to recover the remote sensed hyperspectral image. The main advantage of the proposed methodology for compressing remote sensed hyperspectral images is that the compression process, which must be performed on-board, becomes very simple, being the fusion process used to reconstruct image the more complex one. An extra advantage is that the compression ratio can be fixed in advanced. Many simulations have been performed using different fusion algorithms and different methodologies for degrading the hyperspectral image. The results obtained in the simulations performed corroborate the benefits of the proposed methodology.