The literature has widely acknowledged the impact of the COVID-19 pandemic on the mental health of young adults. Despite extensive research, eudaimonic well-being, which focuses on self-knowledge and self-realization, has been scarcely investigated. This cross-sectional study aimed to add knowledge on the eudaimonic well-being of young adults one year after the outbreak of the COVID-19 pandemic, verifying its potential linkages with fear of death and psychological inflexibility. A total of 317 young Italian adults (18–34 years), recruited through a chain sampling method, completed measures of psychological inflexibility, fear of death, and eudaimonic well-being included in an online survey. The study’s hypotheses were tested with multivariate multiple regression and mediational analyses. Results showed that psychological inflexibility was negatively associated with all the dimensions of well-being, while fear of the death of others was associated with autonomy, environmental mastery, and self-acceptance. Furthermore, in the association between fear of death and well-being, the mediation role of psychological inflexibility was verified. These results contribute to the extant literature on the factors associated with eudaimonic well-being, providing clinical insights into the work with young adults within challenging times.