Adaptive Body Biasing (ABB) is a popularly used technique to mitigate the increasing impact of manufacturing process variations on leakage power dissipation. The efficacy of the ABB technique can be improved by partitioning a design into a number of "body-bias islands," each with its individual body-bias voltage. In this paper, we propose a system-level leakage variability mitigation framework to partition a multiprocessor system into body-bias islands at the processing element (PE) granularity at design time, and to optimally assign body-bias voltages to each island post-fabrication. As opposed to prior gate- and circuit-level partitioning techniques that constrain the global clock frequency of the system, we allow each island to run at a different speed and constrain only the relevant system performance metrics - in our case the execution deadlines. Experimental results show the efficacy of the proposed framework in reducing the mean and standard deviation of leakage power dissipation compared to a baseline system without ABB. At the same time, the proposed techniques provide significant runtime improvements over a previously proposed Monte-Carlo based technique while providing similar reductions in leakage power dissipation.