This paper reports a higher-order analytic energy operator (HO-AEO) approach to monitoring bearing health conditions from vibrations signals that are polluted by strong noise and multiple interferences. The proposed analytic energy operator (AEO) is formed using the raw signal, its Hilbert transform, and their derivatives. In analogy to the conventional energy operator (EO), it represents an alternative energy transformation. However, unlike the conventional EO, it exploits the information from both the real and imaginary parts of the analytic signal. It can also extract both the amplitude and frequency modulations and is thus well suited for detecting impulsive fault signature. The joint use of multiple higher-order AEOs can further offset noise effect. The built-in amplitude demodulation (AD) capability of the proposed HO-AEO eliminates the enveloping step required by most high-frequency resonance (HFR) methods. The method is simple and easy to implement. Our simulation and experimental results have demonstrated that the proposed method can effectively extract bearing fault signature in the presence of heavy noise and multiple vibration interferences. It has also been shown mathematically that the HO-AEO processed signal yields higher signal-to-interference ratio (SIR) than the conventional EO does. The simulation and experimental comparisons also indicate that the proposed method has much better noise and interference handling capabilities than the conventional EO.