A design is presented for the electron cyclotron (EC) heating and current drive system of the ITER upper port launchers based on the remote steering (RS) concept. In this concept the millimeter-wave beam is steered by a mirror that is located at the back end of the launcher waveguide. The RS concept has the advantage that the mirror steering mechanism can be situated in the secondary vacuum of the ITER machine where neutron flux and beryllium and tritium contamination is reduced. This allows simpler maintenance relative to a system with a plasma-facing steering mechanism. The optimization is carried out on the quasi-optical elements of the system, including the mirror shapes and positions. The design is assessed for its effectiveness in stabilizing the neoclassical tearing mode (NTM) over a wide range of ITER reference scenarios. The stabilization performance is quantified in terms of the parameter ntm, expressing the ratio between the peak EC wave-driven current density and the bootstrap current density, which parameter should exceed 1.2. The performance is also evaluated in terms of beam-focusing properties and power loading on the mirrors, and an empirical relation between beam size and ntm has been established. The performance achieved meets the requirements for NTM stabilization in all but one of the ITER reference scenarios.