Objective: The electroencephalogram (EEG) is an essential neuro-monitoring tool for both clinical and research purposes, but is susceptible to a wide variety of undesired artifacts.Removal of these artifacts is often done using blind source separation techniques, relying on a purely data-driven transformation, which may sometimes fail to sufficiently isolate artifacts in only one or a few components.Furthermore, some algorithms perform well for specific artifacts, but not for others.In this paper, we aim to develop a generic EEG artifact removal algorithm, which allows the user to annotate a few artifact segments in the EEG recordings to inform the algorithm.Approach: We propose an algorithm based on the multichannel Wiener filter (MWF), in which the artifact covariance matrix is replaced by a low-rank approximation based on the generalized eigenvalue decomposition.The algorithm is validated using both hybrid and real EEG data, and is compared to other algorithms frequently used for artifact removal.Main results: The MWF-based algorithm successfully removes a wide variety of artifacts with better performance than current state-of-the-art methods.Significance: Current EEG artifact removal techniques often have limited applicability due to their specificity to one kind of artifact, their complexity, or simply because they are too "blind".This paper demonstrates a fast, robust and generic algorithm for removal of EEG artifacts of various types, i.e. those that were annotated as unwanted by the user.