Accurate monitoring of the depth of anesthesia (DoA) is essential for intraoperative and postoperative patient's health. Commercially available electroencephalograph (EEG)-based DoA monitors are recommended only for certain anesthetic drugs and specific age-group patients. This paper presents a machine learning classification processor for accurate DoA estimation irrespective of the patient's age and anesthetic drug. The classification is solely based on six features extracted from EEG signal, i.e., spectral edge frequency (SEF), beta ratio, and four bands of spectral energy (FBSE). A machine learning fine decision tree classifier is adopted to achieve a four-class DoA classification (deep, moderate, and light DoA versus awake state). The feature selection and the classification processor are optimized to achieve the highest classification accuracy for the state of moderate anesthesia required for the surgical operations. The proposed 256-point fast Fourier transform accelerator is implemented to realize SEF, beta ratio, and FBSE that enables minimal latency and high accuracy feature extraction. The proposed DoA processor is implemented using a 65 nm CMOS technology and experimentally verified using field programming gate array (FPGA) based on the EEG recordings of 75 patients undergoing elective surgery with different types of anesthetic agents. The processor achieves an average accuracy of 92.2% for all DoA states, with a latency of 1s The 0.09 mm2 DoA processor consumes 140nJ/classification.