The Norway youth international has signed for the remainder of the W-League season after previously spending three years in the Norwegian Toppserien competition.
"The opportunity to go abroad and play at the highest level in a league that is highly rated was very appealing to me," Eckhoff said.
"I hope to add more power in the midfield and make sure our team stays compact in defence and in balance when attacking."
"As our last signing for this campaign, Noor will add experience and aggressiveness to our midfield," City football director Michael Petrillo said.
"She is a Norwegian youth international, experienced in a top European competition, technically adept and is a proven winner."
Eckhoff won't be available for Sunday's derby rematch as she is in hotel quarantine in Perth until Jan. 20, the day before City's away game against Adelaide United.