This work addresses the problem of noise reduction in tape recordings using a deep-learning approach. First, we build a data set of audio snippets of tape noise extracted from different functional tape equipment—comprising open reel and cassette. Then, we adapt and train an existing deep-learning architecture originally proposed to remove noise from 78 RPM gramophone records. The model learns from mixtures of the noise snippets with clean audio excerpts at different SNRs. Experimental results validate the approach, showing the benefits of using real tape recording noise in training the model. Furthermore, the data set of tape noise snippets and the trained deep-learning models are publicly available. In this way, we encourage the collective improvement of the data set and the broad application of the denoising approach by sound archives.