If you are a citizen of a non-EU country and want to move to a family member in Sweden, you require a residence permit. You can be granted a residence permit if you are married to, have entered into a partnership with, or are the cohabiting partner of someone in Sweden. The family member in Sweden must be a Swedish citizen, have a permanent residence permit, permanent right of residence or a permanent residence card.

If granted a residence permit, a US citizen can enter Sweden with the decision letter from the Migration Agency, and then submit the biometric data for the residence permit card in Sweden.

If you require a visa in order to travel to Sweden, you will need to submit your biometric data at the Embassy and obtain your residence permit card before travelling to Sweden. 

Read more about the application process at the Swedish Migration Agency's website​.