As technology scales, the delay uncertainty caused by process variations has become increasingly pronounced in deep submicron designs. As a result, a paradigm shift from deterministic to statistical design methodology at all levels of the design hierarchy is inevitable . In this paper, we propose a variation-aware task allocation and scheduling algorithm for Multiprocessor System-on-Chip (MPSoC) architectures to mitigate the impact of parameter variations. A new design metric, called performance yield and defined as the probability of the assigned schedule meeting the predefined performance constraints, is used to guide the task allocation and scheduling procedure. An efficient yield computation method for task scheduling complements and significantly improves the effectiveness of the proposed variation-aware scheduling algorithm. Experimental results show that our variation-aware scheduler achieves significant yield improvements. On average, 45% and 34% yield improvements over worst-case and nominal-case deterministic schedulers, respectively, can be obtained across the benchmarks by using the proposed variation-aware scheduler.