Currently, there is a broad portfolio of agile approaches to software development, however, in many cases their implementation is done informally and without a proper institutionalization of the agile values and principles. Although there are some proposals related to the adoption and assessment of agile approaches, efforts have been made without having a common terminology which has led to confusion and terminological conflict affecting the implementation of these approaches in organizations. This article proposes the ontology called OntoAgile, which aims to suggest a common and consistent terminology that allows sharing the knowledge generated around the implementation of the agile approaches in the software processes in a generic and formal way. Similarly, OntoAgile facilitates the assessment of the agility of the software processes from the identification of the relationships between the elements of the software processes and the agile principles and values. OntoAgile was assessed satisfactorily by three cases of application.