This paper presents a streaming system design paradigm that allows developers to model streaming applications and their FPGA-based many-core hardware architectures as processes and channels. We have developed a programming language called System-Oberon, together with a run-time library, a hardware library implemented on an FPGA, and a compiler to automate the system design flow. In general, the proposed paradigm represents a software-driven approach to the streaming system designs on FPGAs. Compared to the existing solutions, our system design paradigm and its tool chain allow the automatic construction of a completely autonomous system on an FPGA, support the task-level parallelism from both software and hardware levels, and avoid the need for hardware programming work for application developers. These features make the proposed approach advantageous in achieving better results regarding the system's performance, power consumption, design reuse and time-to-market. To prove the applicability of our approach, a monitor for real-time ECG signal analysis was built and analyzed for its performance, size, power consumption and development time.