In this paper, we develop an analytical channel model for intelligent reflecting surface (IRS)-assisted free space optical (FSO) systems. Unlike IRS-assisted radio frequency systems, where it is typically assumed that a plane wave is incident on the IRS, in FSO systems, the incident wave is a Gaussian beam with non-uniform power distribution across the IRS. Taking this property into account, we develop an analytical end-to-end channel model for IRS-assisted FSO systems based on the Huygens-Fresnel principle. Our analytical model reveals the impact of the size, position, orientation, and phase-shift configuration of the IRS on the end-to-end channel. Furthermore, we show that results obtained based on geometric optics under the far-field approximation are only valid for a specific range of IRS-receiver lens distances depending on the IRS size, incident beam width, and wavelength. Simulation results validate the accuracy of the proposed analytical results for the FSO beam reflected from the IRS and compare the bit error rate performance obtained for the proposed analytical channel model with that obtained for geometric optics under the far-field approximation.