Recently, research on the potential use of Free Space Optical (FSO) links as a robust communication link between Unmanned Aerial Vehicles (UAVs) has garnered significant attention in academia and industry. Due to the increasing demand for UAV-based FSO links compared to traditional ground-based FSO links, the optimal design of FSO system parameters based on UAVs (such as optimal values for beam divergence angle, optical detector size, receiver lens aperture, transmission power, and many others) is more challenging and crucial than its ground-based counterpart. Furthermore, to avoid the timeconsuming Monte Carlo simulations, the presence of a simple and analytically tractable channel model is crucial and necessary. In this article, to address this need, a new channel model is developed for the desired system under the influence of atmospheric turbulence conditions. Specifically, for weak turbulence conditions, a new channel model based on the Log-Normal atmospheric turbulence channel is proposed. Subsequently, for moderate to strong turbulence conditions, a statistical channel model with a closed-form expression for the Gamma-Gamma turbulence channel is extracted. These proposed channel models, despite their simplicity and analyzability, incorporate the combined effects of atmospheric turbulence and pointing errors. They also account for limitations in the receiver's field of view and inherent position and orientation deviations of UAVs. Furthermore, to analyze performance metrics more effectively, closed-form expressions for outage probability and Bit Error Rate (BER) are derived. Finally, the validity of the proposed new channel models and the derived outage probability and BER expressions are confirmed using Monte Carlo simulations. The developed results can serve as benchmarks for finding optimal adjustable parameters for UAV-based FSO links under various channel conditions and different levels of UAV instability, without the need for time-consuming Monte Carlo simulations.