Modern-day digital hearing aids are prone to an unavoidable acoustic feedback phenomenon, degrading sound quality and speech intelligibility. The linear adaptive feedback cancellation (AFC) systems based on finite-impulse-response filters do not yield satisfactory performance under nonlinearity encountered in the feedback path. In an endeavor to overcome this, a de-correlated improved adaptive exponential functional link adaptive filter (DI-AEF)-based nonlinear AFC (NAFC) system is developed in this paper. It utilizes cross terms of the input samples and trigonometrical expansion with exponentially varying amplitude. To save computations, the delayed outputs of the feedback canceler are appended at the input layer, inspired by the IIR filtering technique. The adaptive de-correlation filter is updated by variable convergence and forgetting factor windowed recursive least square algorithm to address the biased estimation problem. The corresponding update rules, convergence, and bounded-input bounded-output stability conditions have been derived. Extensive simulation results demonstrate the efficacy of the proposed NAFC system for real input signals in terms of perceptual evaluation of speech and audio quality and added stable gain (ASG). The DI-AEF-based system achieves nearly 4-dB improvement in ASG while consuming 53% and 37% less multiplications and additions than the existing nonlinear methods.