In this paper, using the theory of input saturation, a novel path following guidance law for fixed-wing unmanned aerial vehicles (UAVs) is developed. The proposed guidance law is adapted from a pursuit plus line-of-sight guidance law. Furthermore, it employs inertial speed for computing the acceleration commands which adds an adaptive capability of accommodating vehicle speed changes due to external disturbances such as wind. The guidance law is initially developed for two-dimensional (2D) environments which enables vehicles to follow straight lines, circles, and ellipses in planar spaces. Lyapunov theory is used to establish its stability properties, followed by a comparative study with existing algorithms, proposed for 2D environments, to establish its efficacy. The guidance law is then extended for the case of three-dimensional (3D) environments, and appropriate simulation studies are performed. Finally, real-world flight tests for 2D as well as 3D cases are presented, establishing the applicability of the proposed law on UAVs.