Having been predominantly observed in rigid metal and metal alloys since 1865, the magnetoelastic effect was recently experimentally discovered in a soft matter system and used as a new working mechanism for energy and health care applications. Here, a theoretical framework is presented and proven to be universally accurate and robust in interpreting the giant magnetoelastic effect across soft systems subjected to various deformation modes, micromagnet concentrations, magnetization profiles, and geometric structures. The theory uncovers substantial, unique magnetoelastic phenomena in soft systems, including the magnetic pole reversal under localized compression. This work lays a firm foundation for an in-depth understanding and practical applications of the giant magnetoelastic effect in soft matter systems.