To address the stable formation tracking problem of quadrotor unmanned aerial vehicles (UAVs) under external wind disturbances and internal unmodeled dynamics, a predefined-time nonsingular adaptive anti-disturbance formation control method based on radial basis function (RBF) neural networks is proposed. First, a predefined-time reference signal estimator is constructed to generate and adjust the desired trajectory. Then, a predefined-time filter is introduced into the virtual control law, and a continuously differentiable switching function is designed to avoid the singularity issue caused by power-integrator terms in conventional backstepping. Furthermore, RBF neural networks are employed to approximate the unmodeled dynamics, while a predefined-time disturbance observer is developed to jointly estimate and compensate for wind disturbances and neural network approximation errors. Finally, through a hierarchical design consisting of the reference estimator, position-loop controller, and attitude-loop controller, predefined-time stable formation tracking of quadrotor UAVs is achieved. Simulation results demonstrate that fast convergence and strong robustness against wind disturbances and uncertainties are ensured, thereby validating the effectiveness and superiority of the proposed control strategy.