Recent developments in embedded hardware have empowered human experiences through pervasive computing. While embedded systems are becoming more powerful, they still fall short when faced with users' growing desire for running more resource-demanding applications. To bridge this gap, one solution is to leverage powerful resources residing at remote sites by performing computation offloading. Unfortunately, the state-of-the-art offloading frameworks cannot be applied in many embedded systems supporting applications with soft real-time (SRT) constraints or high delay sensitivity, as they typically optimize response times on a 'best-effort' basis using heuristics. This paper establishes a soft real-time offloading framework that optimizes the resource utilization of the embedded system while analytically guaranteeing SRT schedulability. The key idea behind the proposed framework is to view offloading-induced delays as suspensions occurring at the local embedded system side, which allows a task being offloaded to be modelled as a suspending task and thus existing SRT suspension-aware scheduling and analysis techniques to be leveraged. Based on this idea, we propose an offloading algorithm, namely Real-time Offloading Decision-making Algorithm (RODA), to make offloading decisions such that SRT schedulability of the task system can be ensured. The optimality properties of RODA have been proved on both uniprocessors and multiprocessors. We conducted extensive simulations on evaluating schedulability and implemented a case study offloading system on top of real hardware to test runtime response time performance. Results demonstrated that RODA is superior to existing performance-driven offloading algorithms, particularly under heavy workloads.