The dynamic partial reconfiguration (DPR) feature offered by modern FPGAs provides the flexibility of adapting the underlying hardware according to the needs of a particular situation at runtime, in response to application requirements. In recent times, DPR along with drastically reduced reconfiguration overheads has allowed the possibility of scheduling multiple real-time applications on FPGA platforms. However, in order to effectively harness the computation capacity of an FPGA floor, efficient techniques which can schedule real-time applications over both space and time are required. It may be noted that safety-critical systems often require resource-optimal solutions to reduce size, weight, cost and power consumption of the system. However, the scheduling of real-time tasks on FPGAs in the presence of non-negligible reconfigurationlcontext-switching overheads requires careful exploration of the state space which often makes it prohibitively expensive to be applied on-line. Hence, off-line formal approaches are often preferred in the design of reconfiguration controllers (i.e., schedulers) that are correct-by-construction as well as optimal in terms of usage of resources. In this paper, we propose a formal scheduler synthesis framework that generates an optimal scheduler for a set of non-preemptive periodic real-time tasks executing on a FPGA platform. We show the practical viability of our proposed framework by synthesizing schedulers for real-world benchmark applications and implementing them on FPGAs.