The New Horizons (NH) Radio Science Experiment, REX, is designed to determine the atmospheric state at the surface of Pluto and in the lowest few scale heights. Expected absolute accuracies in n, p, and T at the surface are 4⋅10¹⁹ m⁻³, 0.1 Pa, and 3 K, respectively, obtained by radio occultation of a 4.2 cm-λ signal transmitted from Earth at 10–30 kW and received at the NH spacecraft. The threshold for ionospheric observations is roughly 2⋅10⁹ e⁻ m⁻³. Radio occultation experiments are planned for both Pluto and Charon, but the level of accuracy for the neutral gas is expected to be useful at Pluto only. REX will also measure the nightside 4.2 cm-λ thermal emission from Pluto and Charon during the time NH is occulted. At Pluto, the thermal scan provides about five half-beams across the disk; at Charon, only disk integrated values can be obtained. A combination of two-way tracking and occultation signals will determine the Pluto system mass to about 0.01 percent, and improve the Pluto–Charon mass ratio. REX flight equipment augments the NH radio transceiver used for spacecraft communications and tracking. Implementation of REX required realization of a new CIC-SCIC signal processing algorithm; the REX hardware implementation requires 1.6 W, and has mass of 160 g in 520 cm³. Commissioning tests conducted after NH launch demonstrate that the REX system is operating as expected.