FPGA based heterogeneous System On Chips (SOCs) have become a prospective processing platform for modern performance-sensitive systems, like automotive, avionics, chemical reactor etc. In such system, “makespan” time minimization plays a crucial role to achieve higher throughput as well as performance efficiency and thus, efficient task allocation schemes are indeed essential. This paper presents two task allocation algorithms for such FPGA based heterogeneous SOCs. The first allocation strategy is based on well known “Branch and Bound” optimization technique. Secondly, we proposed a novel heuristic based allocation mechanism, TAMF (Task Allocation Mechanism for FPGA based heterogeneous SOC). The simulation based experimental results reveal that both the strategies are able to provide lower makespan time over various simulation scenarios with acceptable runtime overheads. Achieved simulation results are further tested through a validation, carried out on practical ZYNQ SOC platform using standard benchmark task sets.