With the rapid development of Industrial 4.0, massive emerging time-critical applications pose new demands for industrial networks, such as strict latency boundaries, ultra-reliable transmission, and so on. Time-Sensitive Networking (TSN) is well suited for these demanding scenarios due to its support for deterministic transmission based on Ethernet. However, many use cases in real industrial scenarios involve non-TSN domains, and, thus, the network requires providing deterministic transmission across non-TSN domains to support them. To this end, this paper proposes a novel Software-Defined Time-Sensitive Networking (SD-TSN) framework that integrates the determinism of TSN and scalability of Software-Defined Networking (SDN). SD-TSN exploits the coordination between the coordinated controller and different domain controllers to bound non-deterministic queuing delays in a way that guarantees determinism. In particular, we designed a multi-domain time-aware traffic scheduling model, which harmonizes the time-aware shaper (TAS) in TSN and time-slots in non-TSN domains based on a global view, generating transmission schedules for each domain. A prototype testbed was built to conduct the experiments. The evaluation results demonstrate that the proposed method can efficiently achieve bounded delay and low delay variations in the transmission across non-TSN domains.