Energy harvesting sensors move into the mainstream because they are regarded as a perfect match for the monitoring applications. Nonetheless, their implementation is only feasible if the computing unit, generally a microcontroller, is capable of running the real-time tasks using sophisticated scheduling and power management techniques. In this paper, we address the hard real-time scheduling problem of Directed Acyclic Graph (DAG) tasks in a uniprocessor RTEH (Real Time Energy Harvesting) computing system. In this model, a task is defined as a set of dependent sub-tasks that execute under precedence constraints with processing time and energy requirements. We demonstrate that the energy aware ED-H algorithm provides an optimal solution. We show that the scheduling policy directly includes a feasibility analysis by enforcing the precedence constraints, thus making it possible to get rid of semaphore synchronization.