Global trends that occur in various fields of knowledge with a significant acceleration affect the development of information technology and project management competencies, programs, and project portfolios. The paper aims to develop and study information technology and mechanisms for assessing the competencies of project managers for their development based on current trends and flexible methodology of Agile in project management in creating modern information and communication technologies in project management. Global trends that challenge the development of project management competencies and programs are related to global acceleration, digitalization of society, development of blockchain, cloud and fog technologies, active introduction of smart systems, the transition from “Rational economy” to “Behavioral economy”, “Green economy”, “Sustainable development economy” and “Circular economy”. The convergence of these trends creates a new platform for the effective application of existing methodologies, knowledge systems, and methods of assessing the competence of project managers. Based on convergence, integration, and harmonization of project and program management methodologies, step-by-step research methods have been identified. The formation of an updated system of competencies lies in the change of paradigms from the traditional waterfall life cycle model to the Agile life cycle models of the projects. Decisionmaking in conditions of uncertainty based on data mining, from rational to irrational forms. The article examines modern hybrid information models of projects and programs that change the competency systems of project managers, convergent models and methods of decision making. At the same time, the change in competencies as actions or functions to be performed by project managers affects the competency model and evaluation system, including key competency indicators. A meaningful model of diagnostics of application of competence models and methods of project management in the digital and “behavioral economy” based on flexible methodologies is given. Some key competency indicators that are used in assessing the competence of a project manager based on his competencies in working in a project team are identified. Patterns of behavior of project managers in project product creation and project management are studied. The patterns allowed the authors to identify bottlenecks in the application of Agile project management methodologies in the convergence of trend information models and technologies. An example of information technology for managing the assessment of competence of project managers according to the IPMA Agile ICB model is given.