Background: COVID-19 vaccines are one of the most effective preventive strategies for containing the pandemic. Having a better understanding of the public's conceptions of COVID-19 vaccines may aid in the effort to promptly and thoroughly vaccinate the community. However, because no empirical research has yet fully explored the public's vaccine awareness through sentiment–based topic modeling, little is known about the evolution of public attitude since the rollout of COVID-19 vaccines. Objective: In this study, we specifically focused on tweets about COVID-19 vaccines (Pfizer, Moderna, AstraZeneca, and Johnson & Johnson) after vaccines became publicly available. We aimed to explore the overall sentiments and topics of tweets about COVID-19 vaccines, as well as how such sentiments and main concerns evolved. Methods: We collected 1,122,139 tweets related to COVID-19 vaccines from December 14, 2020, to April 30, 2021, using Twitter's application programming interface. We removed retweets and duplicate tweets to avoid data redundancy, which resulted in 857,128 tweets. We then applied sentiment–based topic modeling by using the compound score to determine sentiment polarity and the coherence score to determine the optimal topic number for different sentiment polarity categories. Finally, we calculated the topic distribution to illustrate the topic evolution of main concerns. Results: Overall, 398,661 (46.51%) were positive, 204,084 (23.81%) were negative, 245,976 (28.70%) were neutral, 6899 (0.80%) were highly positive, and 1508 (0.18%) were highly negative sentiments. The main topics of positive and highly positive tweets were planning for getting vaccination (251,979/405,560, 62.13%), getting vaccination (76,029/405,560, 18.75%), and vaccine information and knowledge (21,127/405,560, 5.21%). The main concerns in negative and highly negative tweets were vaccine hesitancy (115,206/205,592, 56.04%), extreme side effects of the vaccines (19,690/205,592, 9.58%), and vaccine supply and rollout (17,154/205,592, 8.34%). During the study period, negative sentiment trends were stable, while positive sentiments could be easily influenced. Topic heatmap visualization demonstrated how main concerns changed during the current widespread vaccination campaign. Conclusions: To the best of our knowledge, this is the first study to evaluate public COVID-19 vaccine awareness and awareness trends on social media with automated sentiment–based topic modeling after vaccine rollout. Our results can help policymakers and research communities track public attitudes toward COVID-19 vaccines and help them make decisions to promote the vaccination campaign. J Med Internet Res 2022;24(2):e31726 doi:10.2196/31726 [ABSTRACT FROM AUTHOR]