The 27-year-old has written a contract for two years with the possibility of extension for another year.
"I'm so happy to be here and look forward to getting started and becoming a part of this family. I have followed Manchester United in recent years and I'm very impressed," she says in a statement.
Zigiotti Olme has made 47 international matches for Sweden and played an important role during the summer's European Championship where Sweden reached the quarterfinals. The midfielder has previously represented, among others, Häcken and Hammarby in Sweden.
I took big steps in my development with Bayern München during the year there and am grateful for the time. But I'm very happy about this opportunity with United too, I want a bigger role in a team than being a substitute, she says to Aftonbladet.
Zigiotti Olme won both the German league and the domestic cup last season but now hopes to get a bigger role in her new club.
