The unmanned aerial vehicle (UAV) formation flying process will be affected by external gusts, internal parameter perturbations, unmodeled dynamics and other multi-source disturbances. In addition, during the formation dynamic adjustment stage, the large change of formation error may lead to safety problems such as collision. This paper proposes an active disturbance rejection formation control of UAVs based on prescribed performance to attenuate the multi-source disturbances’ influence and guarantees the satisfaction of formation error. By introducing a novel prescribed performance algorithm based on the hyperbolic tangent function, the proposed method ensures that the formation error converges within the preset envelope and meets the dynamic constraint of formation error without requiring initial state information of the formation system. Through the introduction of a generalized proportional integral observer (GPIO), the estimation and compensation of high-order time-varying disturbances in a formation system are realized, the types of disturbances which can be handled are broadened, and the control accuracy of the formation system is improved.