Conversational agents (CAs), also known as chatbots, are digital dialog systems that enable people to have a text-based, speech-based, or nonverbal conversation with a computer or another machine based on natural language via an interface. The use of CAs offers new opportunities and various benefits for health care. However, they are not yet ubiquitous in daily practice. Nevertheless, research regarding the implementation of CAs in health care has grown tremendously in recent years. This review aims to present a synthesis of the factors that facilitate or hinder the implementation of CAs from the perspectives of patients and health care professionals. Specifically, it focuses on the early implementation outcomes of acceptability, acceptance, and adoption as cornerstones of later implementation success. We performed an integrative review. To identify relevant literature, a broad literature search was conducted in June 2021 with no date limits and using all fields in PubMed, Cochrane Library, Web of Science, LIVIVO, and PsycINFO. To keep the review current, another search was conducted in March 2022. To identify as many eligible primary sources as possible, we used a snowballing approach by searching reference lists and conducted a hand search. Factors influencing the acceptability, acceptance, and adoption of CAs in health care were coded through parallel deductive and inductive approaches, which were informed by current technology acceptance and adoption models. Finally, the factors were synthesized in a thematic map. Overall, 76 studies were included in this review. We identified influencing factors related to 4 core Unified Theory of Acceptance and Use of Technology (UTAUT) and Unified Theory of Acceptance and Use of Technology 2 (UTAUT2) factors (performance expectancy, effort expectancy, facilitating conditions, and hedonic motivation), with most studies underlining the relevance of performance and effort expectancy. To meet the particularities of the health care context, we redefined the UTAUT2 factors social influence, habit, and price value. We identified 6 other influencing factors: perceived risk, trust, anthropomorphism, health issue, working alliance, and user characteristics. Overall, we identified 10 factors influencing acceptability, acceptance, and adoption among health care professionals (performance expectancy, effort expectancy, facilitating conditions, social influence, price value, perceived risk, trust, anthropomorphism, working alliance, and user characteristics) and 13 factors influencing acceptability, acceptance, and adoption among patients (additionally hedonic motivation, habit, and health issue). This review shows manifold factors influencing the acceptability, acceptance, and adoption of CAs in health care. Knowledge of these factors is fundamental for implementation planning. Therefore, the findings of this review can serve as a basis for future studies to develop appropriate implementation strategies. Furthermore, this review provides an empirical test of current technology acceptance and adoption models and identifies areas where additional research is necessary. PROSPERO CRD42022343690; https://www.crd.york.ac.uk/prospero/display_record.php?RecordID=343690.