This paper proposes a model predictive control scheme for a class of constrained nonlinear time-delay systems with guaranteed closed-loop asymptotic stability. Asymptotic stability of the closed-loop is guaranteed by utilizing an appropriate terminal cost functional and an appropriate terminal region. A novel structured procedure is derived to determine the terminal cost and the terminal region offline. For this purpose, a combination of Lyapunov-Krasovskii and Lyapunov-Razumikhin arguments is used to compute a locally stabilizing controller. The resulting conditions are formulated in terms of linear matrix inequalities.