Andreatta will take over from interim head coach Mick McArdle after Scotland suffered their fourth straight loss in the current Women's Nations League campaign on Tuesday - a 6-1 rout by Germany.
Andreatta had played an important role in helping Australia reach the semi-finals at the Tokyo Olympics and 2023 World Cup, Football Australia said in a statement confirming her departure.
"I'm absolutely delighted," Andreatta said in a statement.
"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."