The relevance of the research is associated with the fact that information technologies, social services of the Internet and the very cyberspace are changing rapidly adding into the human life new facets of existence and interaction, new opportunities to act, manifestations of mental processes and personality features, one of them being information competency. These changes affect the way the understanding of such phenomena as Internet activity and Internet addiction throughout the development of one’s information competency is shaped. With regard to this, the paper is aimed at finding out the signs of Internet activity and its transition into Internet addiction in the development of an individual’s information competency. The leading methods for researching this problem are extrapolation and modeling that allow considering the approaches to understanding the “Internet activity” and “Internet addiction” phenomena in pedagogical and psychological literature in their entirety and in comparison, analyzing the Internet risks, and describing the mechanisms of transformation of Internet activity into Internet addiction during the development of an individual’s information competency. In the paper, the following phenomena are defined: the “Internet activity” as a part of daily culture of a person belonging to digital society and the “Internet addiction” as acquired behavior based on the intensity of the wish to stay in the Internet continuously and affecting the development of an individual’s information competency in the context of changing its role both in the real and virtual life. In the paper, it is emphasized that a certain development level of an individual’s information competency is manifested in the individual’s Internet activity while excessive Internet activity practiced by the individual triggers the mechanisms of its transformation into Internet addiction. The materials of the paper are of practical importance for master’s degree students, postgraduate students, teachers of higher education institutions and teachers of educational institutions conducting research in this area that set objectives associated with looking for pedagogical means for individuals to practice their Internet activity without running into Internet addiction.