Social distancing and the use of masks are crucial to prevent the spread of SARS-COV-2. Knowledge of the determinants of this behavior is essential to promote effective communication with the public in future public health crises that require mass public compliance with preventive behaviors. This systematic review focused on scientific evidence related to cognitive factors that underlie the intention of young adults’ intention to adhere to preventive social behavior (distancing and/or the use of facial masks) against COVID-19. A systematic literature search on the electronic database, PubMed, Scopus, Web of Science, and EBSCO was performed in December 2022 according to Preferred Reporting Items for Systematic Reviews and Meta-Analysis guidelines. The PEO (Population: young adults, Exposure: COVID-19, and Outcome: cognitive factors that underlie the intention of young adults to adhere to social distancing and/or the use of facial masks) was developed to identify search terms and inclusion/exclusion criteria. Eight studies met the eligibility criteria. None of the studies were seriously flawed according to the quality assessment, and they were considered to have a low risk of bias for selection. Several cognitive determinants emerged in the analysis. For both social distancing and the use of masks, the most relevant factors related to adherence include risk perception and perceived severity, the moral value of fairness, social responsibility, trust in the government, respect for authority, and the quality of institutional communication. Adherence to social distancing was found related to self-efficacy. These results reinforce social cognitive models showing the relevance of cognitions to adherence behavior, and highlight the responsibility of official institutions in the development of contexts and in adapting the communication for the effective promotion of adherence to the recommendations they launch.