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The challenge of wildfire management and detection is recently gaining increased attention due to the increased severity and frequency of wildfires worldwide. Popular fire detection techniques such as satellite imaging and remote camera-based sensing suffer from late detection and low reliability while early wildfire detection is a key to prevent massive fires. In this paper, we propose a novel wildfire detection solution based on unmanned aerial vehicles assisted Internet of things (UAV-IoT) networks. The main objective is to (1) study the performance and reliability of the UAV-IoT networks for wildfire detection and (2) present a guideline to optimize the UAV-IoT network to improve fire detection probability under limited budgets. We focus on optimizing the IoT devices' density and number of UAVs covering the forest area such that a lower bound of the wildfires detection probability is maximized within a limited time and budget. At any time after the fire ignition, the IoT devices within a limited distance from the fire can detect it. These IoT devices can then report their measurements only when the UAV is nearby. Discrete-time Markov chain (DTMC) analysis is utilized to compute the fire detection probability at discrete time. Before declaring fire detection, a validation state is designed to account for IoT devices' practical limitations such as miss-detection and false alarm probabilities. Numerical results suggest that given enough system budget, the UAV-IoT based fire detection can offer a faster and more reliable wildfire detection solution than the state of the art satellite imaging techniques.