Information provided from a single spectral band of a satellite image, may not be sufficient in most cases for classification, recognition and change detection applications. Therefore, bands with different spectral and spatial characteristics are combined to obtain a single fused image that contains complementary information. This study introduces a novel hybrid fusion method for remotely sensed infrared and visible images based on backtracking search algorithm (BSA) and Shearlet transform. Shearlet is an efficient processing method to transform spatial information and BSA is a powerful metaheuristic optimization method. Combining these techniques offers an efficient way to fuse low-resolution infrared and high-resolution panchromatic bands of satellite images. Extensive experiments proved that proposed method outperforms well-known multi-scale transforms based fusion methods in terms of both numerical and visual evaluations.