Over the past few decades, large archives of paper-based historical documents, such as books and newspapers, have been digitized using the Optical Character Recognition (OCR) technology. Unfortunately, this broadly used technology is error-prone, especially when an OCRed document was written hundreds of years ago. Neural networks have shown great success in solving various text processing tasks, including OCR post-correction. The main disadvantage of using neural networks for historical corpora is the lack of sufficiently large training datasets they require to learn from, especially for morphologically-rich languages like Hebrew. Moreover, it is not clear what are the optimal structure and values of hyperparameters (predefined parameters) of neural networks for OCR error correction in Hebrew due to its unique features. Furthermore, languages change across genres and periods. These changes may affect the accuracy of OCR post-correction neural network models. To overcome these challenges, we developed a new multi-phase method for generating artificial training datasets with OCR errors and hyperparameters’ optimization for building an effective neural network for OCR post-correction in Hebrew. To evaluate the proposed approach, a series of experiments using several literary Hebrew corpora from various periods and genres were conducted. The obtained results demonstrate that (1) training a network on texts from a similar period dramatically improves the network's ability to fix OCR errors, (2) using the proposed error injection algorithm, based on character-level period-specific errors, minimizes the need for manually corrected data and improves the network accuracy by 9%, (3) the optimized network design improves the accuracy by 3% compared to the state-of-the-art network, and (4) the constructed optimized network outperforms neural machine translation models and industry-leading spellcheckers. The proposed methodology may have practical implications for digital humanities projects that aim to search and analyze OCRed documents in Hebrew and potentially other morphologically-rich languages.