Former Australia striker Milicic, an assistant coach for the men's team at the last two World Cups, will be tasked with restoring harmony in the world's sixth-ranked team after it was rocked by the dismissal of long-time mentor Stajcic.
The FFA cited a "poor culture" around the team for Stajcic's removal, which followed an internal survey of players and staff, and a supplementary review by a women's rights group.
Milicic, 44, has no experience coaching women at a high level and will have to come up to speed quickly, with the Matildas to face New Zealand on Feb. 28, followed by South Korea and Argentina at the inaugural Cup of Nations tournament on home soil.

Ante Milicic during a Socceroos team training session as part of their 2018 FIFA World Cup training in Turkey. Source: AAP
"It is an honour to be appointed head coach of the ... Matildas and I am determined to make the most of this opportunity together with the squad and staff,” he said in an FFA media release.
"Australia has many fantastic players right now and I know that the squad that is ultimately selected will be eager to seize its chance in France."
Stajcic, who guided the Matildas to the quarter-finals of the 2015 World Cup, was considered popular with his players and a number of them expressed dismay over his sacking.
Veteran forward and former co-captain Lisa De Vanna said it would be difficult to adjust quickly after more than four years under him.
"We just have to start all over again," she said before Milicic's appointment was made public.
"It's tough for some, me personally because of my relationship with Stajcic. It's going to be different for me but at the same time, I'll have him in my heart whenever I play an international.
"But there's a goal that I want to achieve and that's to win the World Cup."
Milicic, who has also coached the men's youth squad, is seen as a safe pair of hands and one who knows the Australian football landscape intimately.
"Ante’s intimate involvement with our National Teams Unit over the past five years ensured that he will commence the position with a clear understanding of the systems in place, and with sound relationships with key technical, backroom, and administrative staff already forged," FFA CEO David Gallop said.
The FFA has been pilloried by media pundits and fans over Stajcic's removal, and its recently overhauled board may review its managers' handling of the decision, local media reported.
After declining to comment for nearly three weeks as he considered legal options, Stajcic broke his silence last week to call for an independent inquiry into his termination.
Australia are one of the top six seeded nations at the June 7-July 7 World Cup where they have been drawn with Italy, Jamaica and Brazil in Group C.