This paper presents a new method for run-time management of shared processing resources in multiprocessor systems on chip. A centralized resource manager unit performs dynamic allocation of shared processing resources according to the system state and given constraints. It implements a hardware mutual exclusion so that no inter-processor synchronization is required for accessing the resources. Moreover, it supports dynamic power management. In addition, a hardware implementation of the resource manager is proposed. In a case study, a resource manager is evaluated in a data-parallel MPEG-4 video encoder on multiprocessor system on chip on FPGA. The RM eases the design of six different architectures featuring two to twelve shared hardware accelerators. Only a few accelerators are required for the best performance as the accesses are efficiently scheduled.