According to the Peter principle, in hierarchical organizations all workers sooner or later become incompetent due to being promoted to positions that don't suit them. That is caused by traditional promotion strategies that favor the most successful employees while it does not always happen to be the best approach. On the other hand, applying unconventional promotion policies might result in negative psychological effects, including drop in personnel motivation. General promotion rules also ignore the possibility that the Peter principle may hold for some hierarchical pathways while remaining inactive for other types of promotions. The purpose of this article is to justify the new way of preventing the Peter principle effect by employing machine learning (ML) models to predict workers' potential competence level they would acquire in case of promotion. The article proposes the algorithm of organizational promotions based on the ML approach. The set of employees' characteristics for the models to be trained on, as well as specific ML algorithms, namely linear-based and tree-based are suggested. Inner working specifics of the algorithms are detailed from the mathematical point of view. The principles of the modern ML training process are described and the training data requirements are highlighted. The advantages of employing a dynamic personalized promotion strategy based on machine learning methods are described. Such a strategy allows treating separate promotions individually, choosing from candidates solely on the basis of the model prediction, thus avoiding the unnecessary usage of unconventional policies and subsequent motivational drops. In addition, ML-based approach opens up possibilities to substantiate promotion choices, as those were derived from actual historical data used for training the model. This excludes a potential sense of prejudice while using multiple features for prediction eliminates the risk of unscrupulous employees' behavior aimed at manipulating their own performance with the purpose of receiving a promotion. Properly implemented, the proposed algorithm can help to eliminate the negative effect of the Peter principle while mostly preserving the motivational component of promotions.