Effective educational interventions require sufficient learner engagement, which can be difficult to achieve if the learner is inadequately motivated. Games have been shown to possess powerful motivators that fuel a person's desire to engage in unattractive activities, such as learning theoretical material. However, to design an educational game that is capable of providing motivated engagement is a challenging task. Previous research has proposed various game motivators and game design principles to alleviate this, but a comprehensive synthesis has yet to appear. In this study, we conducted a systematic literature review that yielded two major contributions: (i) a taxonomy of 56 game motivators in 14 classes; and (ii) a taxonomy of 54 educational game design principles in 13 classes, with linkages to the identified game motivators. As a minor contribution, we have also presented a classification of gamification-related terms and proposed different strategies for applying gamification. The results of this study are available for educational game designers and researchers to use as a practical toolkit for the creation and evaluation of motivating educational games that keep players engaged. Moreover, this study is the first step towards the creation of a unified gamification framework.