Vaccines are authorized by the US Food and Drug Administration (FDA). It sets strict standards for clinical trials and carefully reviews scientific data from vaccine developers.
Doctors and medical experts with many years of experience regulating vaccines looked at information about the safety, effectiveness, and quality of the vaccines before making their decision. They determined that the benefits of the vaccines outweigh any known or potential risks. After a vaccine is authorized by the FDA and made available to the public, experts continue to closely monitor it for safety.
SOURCE: https://www.fda.gov/vaccines-blood-biologics/vaccines/emergency-use-authorization-vaccines-explained (FDA)