The multiple phase screens technique is often used for modeling wave propagation and radio occultation sounding of the atmosphere. The last step of this procedure is the propagation from the last phase screen to the observation orbit of the spaceborne receiver. This step was formerly performed by the computation of multiple diffractive integrals, which impairs the numerical efficiency of the algorithm. We introduce an asymptotic method of wave propagation in vacuum from the last phase screen to a generic observation path. The exact solution is written in the form of the Zverev Transform, which belongs to the class of Fourier Integral Operators (FIO). The phase function of such an operator can be derived from the geometric optical equations. We construct an approximation for the Zverev Transform, utilizing the linearization of the equation of the geometric optical ray propagation in the vicinity of a smooth model of the ray structure. This permits the design of a fast numerical algorithm based on an FFT. Numerical simulations are performed for microwave propagation through a model atmosphere based on realistic gridded global fields of meteorological parameters. The new method based on the Linearized Zverev Transform is compared with the standard combination of multiple phase screens and diffractive integrals and with the asymptotic forward modeling for the propagation of centimeter waves in the atmosphere on limb paths. This method is especially useful for modeling LEO–LEO microwave occultations at frequencies of 9–30 GHz. The simulations demonstrate a high accuracy and numerical efficiency of the proposed method.