Andreatta has been assistant coach since 2019, and was appointed lead assistant coach under Tony Gustavsson in 2021.
Andreatta played a crucial role in Australia's run to the semi-finals of both the Tokyo Olympics and the 2023 Women's World Cup, and was also head coach of Australia's first U23 team.
The Queenslander was Brisbane Roar's A-League Women coach from 2016-2018, leading the club to the 2018 premiership, while also working as the Matildas' assistant analyst.
Andreatta's departure adds to a massive overhaul of the Matildas' coaching staff after Young Matildas coach Leah Blayney took up an assistant coach role with Japan earlier this year.
It opens the door for the incoming coach, widely expected to be Lyon boss Joe Montemurro, to bring in their own staff.
"Mel's influence on women's football in Australia at both a domestic and international level has been significant, where she has been instrumental in not only the development of current Matildas but the success of the team over recent years," Football Australia head of national teams Gary Moretti said.
"Mel's appointment as head coach of the Scotland women's national team is not only deserved recognition for her achievements to date but further acknowledgement of the high regard for Australian coaches internationally.
"We would like to thank Mel for her contribution to our women's national teams for more than a decade and wish her all the very best with this new and exciting chapter."
Andreatta joins Tanya Oxtoby (Northern Ireland) among top female Australian coaches heading up other national teams.
Scotland did not qualify for the Women's Euros but will have their eye on reaching the 2027 Women's World Cup.
"I'm absolutely delighted to be leading Scotland women's national team into a new, exciting era," Andreatta said.
"The future is definitely bright and with my extensive coaching, talent development and major tournament experience, my aim is to support the players and staff to reach their fullest potential.
"The ambition is to get Scotland back to consistent qualification and with the squad in a period of transition, this is the perfect opportunity to start building towards that future."
SFA chief executive Ian Maxwell said: "Melissa provided a breadth of different experiences at all levels of the women's game in Australia.
"She is a valued member of the Matildas' coaching staff but also has responsibility for developing elite youth players within a respected performance system.
"I am sure I speak on behalf of the players when I say we are all looking forward to Melissa starting her new role."
Andreatta is expected to be in place, pending her visa, for Scotland's Nations League match against Austria on May 30.
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