https://is.usembassy.gov/iceland-open-to-u-s-citizens-with-proof-of-vaccination/
On March 17, 2021, the Icelandic government announced that all those who have been fully vaccinated against COVID-19 will be allowed to travel to Iceland without being subject to border measures, such as testing and quarantine. Until now, this exemption has only applied to those presenting certificates from the EU/EEA Area but will now apply equally to everyone who can provide proof of a full vaccination with a vaccine that has been certified for use by the European Medical Agency as well as requirements defined by the Chief Epidemiologist of Iceland and Icelandic regulations.
Certificates of vaccination with a vaccine authorized by the European Medicines Agency (EMA), that are listed here (this list is updated as needed). Certificates are accepted wheter they originate from countries within or outside the EEA-area:
1. Comirnaty; Pfizer-BioNTech
2. COVID-19 Vaccine Moderna
3. COVID-19 Vaccine AstraZeneca
4. COVID-19 Vaccine Janssen