Educational artificial intelligence (EAI) refers to the use of artificial intelligence (AI) to support personalized and automated feedback and guidance in the educational field. Inevitably, it serves as a more important part of the educational system in the coming years. However, novel development in this field has been inadequately reviewed and conceptualized in a visualized, objective and comprehensive way. In this view, a bibliometric analysis was conducted to obtain an overview of its trends from publication outputs, countries’ cooperation, cluster analysis, and research evolution. Around 8660 Scopus-published articles from 2000 to 2019 were gathered for analysis using CiteSpace and Alluvial generator. In the study, a growing interest in EAI research and deepening cooperation among countries was first identified, entailing favorable conditions for promoting globalization in this aspect. Afterward, five core clusters were established for the intellectual structure of EAI, including intelligent tutoring system, learning system, student, labeled training data, and pedagogy. The development of EAI research was further conceptualized as follows: (a) technological foundation; (b) technological breakthrough; (c) intelligent application; and (d) symbiotic integration. Finally, three prospective directions for future EAI research were suggested.