It has been recently shown in [Automatica J. IFAC, 29 (1993), pp. 969-983; IEEE Trans. Automat. Control, 39 (1994), pp. 762-779] that time-domain constraints can be incorporated explicitly into H-infinity, optimal control problems over a finite horizon. In this paper, we construct a sequence of such finite-horizon constrained H-infinity optimization problems and show that their solutions converge to the solution of the infinite-horizon H-infinity optimization. We prove that convergence is uniform in the H-infinity norm and that the optimal solution to the infinite-horizon problem is unique.