A receding horizon control (RHC) algorithm for convergent navigation of a differential drive mobile robot is proposed. Its objective function utilizes a local-minima-free navigation function to measure the cost-to-goal over the robot trajectory. The navigation function is derived from the path-search algorithm over a discretized 2-D search space. The proposed RHC navigation algorithm includes a systematic procedure for the generation of feasible control sequences. The optimal value of the objective function is employed as a Lyapunov function to prove a finite-time convergence of the discrete-time nonlinear closed-loop system to the goal state. The developed RHC navigation algorithm inherits fast replanning capability from the D* search algorithm, which is experimentally verified in changing indoor environments. The performance of the developed RHC navigation algorithm is compared with the state-of-the-art sample-based motion planning algorithm based on lattice graphs, which is combined with a trajectory tracking controller. The RHC navigation algorithm produces faster motion to the goal with significantly lower computational costs and it does not need any controller tuning to cope with diverse obstacle configurations.