Companion technologies, such as social robots and conversational chatbots, take increasing responsibility for daily tasks and support our physical and mental health. Especially in the domain of healthcare, where technologies are often applied for long-term use, our experience with and relationship to such technologies become ever more relevant. Based on a 2-week interaction period with a conversational chatbot, our study (N = 58) explores the relationship between humans and technology. In particular, our study focuses on felt social connectedness of participants to the technology, possibly related characteristics of technology and users (e.g., individual tendency to anthropomorphize, individual need to belong), as well as possibly affected outcome variables (e.g., desire to socialize with other humans). The participants filled in short daily and 3 weekly questionnaires. Results showed that interaction duration and intensity positively predicted social connectedness to the chatbot. Thereby, perceiving the chatbot as anthropomorphic mediated the interrelation of interaction intensity and social connectedness to the chatbot. Also, the perceived social presence of the chatbot mediated the relationship between interaction duration as well as interaction intensity and social connectedness to the chatbot. Characteristics of the user did not affect the interrelations of chatbot interaction duration or intensity and perceived anthropomorphism or social presence. Furthermore, we did not find a negative correlation between felt social connectedness of users to the technology and their desire to socialize with other humans. In sum, our findings provide both theoretical and practical contributions. Our study suggests that regular interaction with a technology can foster feelings of social connectedness, implying transferability of dynamics known from interpersonal interaction. Moreover, social connectedness could be supported by technology design that facilitates perceptions of anthropomorphism and social presence. While such means could help to establish an intense relationship between users and technology and long-term engagement, the contexts in which anthropomorphic design is, actually, the means of choice should be carefully reflected. Future research should examine individual and societal consequences to foster responsible technology development in healthcare and beyond.