This paper presents a virtual sensor for the in-process prediction of cutting forces from feed drive current measurements in milling processes via inverse filtering. Components of the feed drive current in ball-screw drives that are related to inertia, friction, and gravity are separated from the cutting-force-related component via models or air-cutting experiments. Impact hammer tests are then used to identify the transfer function between forces at the tool tip and the corresponding response at the feed drive. The proposed inverse filtering approach completes the virtual sensor for online monitoring of cutting forces based on feed drive current signals. Compared to existing approaches, which are mainly based on Kalman-filter or deep learning models, this method avoids the additional effort for modeling, parameter identification and generation of training data. Experimental results are presented for cutting tests on a three-axis turn-milling center. The prediction error between the virtual sensor and the measured cutting forces lies between 6% and 17%, depending on the cutting parameters. In general, the virtual sensor can be implemented in any feed drive system with a minimal effort for parameter identification.