Ute Steyer, 47, will take over the post in January, 2015.
"I'm looking forward to returning to Stockholm after a total of 12 years in Israel and the US," she said in a statement.
Steyer will work in the Stockholm synagogue, together with Cantor Isidoro Abramowicz.
Ute Steyer. Photo: Sweden's Jewish Community
The news was praised by Ingrid Lomfors, the general secretary of the community.
"We're rewriting history for Swedish Jews," she trumpeted. "We've never had a woman in the Rabbi post. It's a change we've longed for and it's a move that's consistent with Sweden's equal society," she said in a statement.
Steyer grew up in London, Athens, and Berlin and came to Sweden first in 1992. She has lived in New York since 2009.
Jews in Sweden have fallen victim to rising religious tensions and increasing anti-Semitism of late. In August, the Swedish government approved a donation of 2 million kronor ($289,166) for increasing security for Jewish congregations.
In October last year, Sweden elected Bishop Antje Jackelén as the country's first female archbishop.