The evolution of artificial intelligence and natural language processing generates new opportunities for conversational agents (CAs) that communicate and interact with individuals. In the health domain, CAs became popular as they allow for simulating the real-life experience in a health care setting, which is the conversation with a physician. However, it is still unclear which technical archetypes of health CAs can be distinguished. Such technical archetypes are required, among other things, for harmonizing evaluation metrics or describing the landscape of health CAs. The objective of this work was to develop a technical-oriented taxonomy for health CAs and characterize archetypes of health CAs based on their technical characteristics. We developed a taxonomy of technical characteristics for health CAs based on scientific literature and empirical data and by applying a taxonomy development framework. To demonstrate the applicability of the taxonomy, we analyzed the landscape of health CAs of the last years based on a literature review. To form technical design archetypes of health CAs, we applied a k-means clustering method. Our taxonomy comprises 18 unique dimensions corresponding to 4 perspectives of technical characteristics (setting, data processing, interaction, and agent appearance). Each dimension consists of 2 to 5 characteristics. The taxonomy was validated based on 173 unique health CAs that were identified out of 1671 initially retrieved publications. The 173 CAs were clustered into 4 distinctive archetypes: a text-based ad hoc supporter; a multilingual, hybrid ad hoc supporter; a hybrid, single-language temporary advisor; and, finally, an embodied temporary advisor, rule based with hybrid input and output options. From the cluster analysis, we learned that the time dimension is important from a technical perspective to distinguish health CA archetypes. Moreover, we were able to identify additional distinctive, dominant characteristics that are relevant when evaluating health-related CAs (eg, input and output options or the complexity of the CA personality). Our archetypes reflect the current landscape of health CAs, which is characterized by rule based, simple systems in terms of CA personality and interaction. With an increase in research interest in this field, we expect that more complex systems will arise. The archetype-building process should be repeated after some time to check whether new design archetypes emerge.