Gustavsson's four-year tenure came to an end after the Swede failed to steer the Matildas out of the group stage at the Paris Olympics.
FA said in a statement that the decision to not extend Gustavsson's up-and-down reign was mutual.
The 50-year-old's future has been a hot topic since last year's Women's Women World Cup on home soil after he was linked with the Swedish men's side and the US women's national team.
Gustavsson opted to see out the final year of his deal with Australia and in a cruel twist of fate it was the US who all-but ended the Matildas' Olympics medal hopes in the early hours of Thursday morning by sealing a 2-1 win.
Australia clung to hope they could squeak through to the quarter-finals in France as a best third-place finisher but results from other groups went against them.
It represents the first time in 24 years that Australia has failed to make it to the knockout stage of the Games.
FA's decision to move quickly has been done with a view to attracting the highest-calibre candidate although the most-likely homegrown contender - former Melbourne Victory coach Joe Montemurro - has recently signed a deal with French club Lyon.
FA will hope that hosting the 2026 Asian Cup will also strengthen their chances of attracting a top-tier coach.
Gustavsson informed his players of his departure in the aftermath of the loss to the USA.
His exit marks the end of a period where the women's game in Australia has undergone an explosion in popularity following the Matildas' run to a fourth-place finish at last year's World Cup.
Gustavsson deserves credit for turning Clare Hunt, Cortnee Vine and Kyra-Cooney Cross into mainstays of the Matildas set-up and backing Mackenzie Arnold as his first-choice goalkeeper.
Those success stories are tempered with concerns over his over-reliance on Australia's golden generation, his inability to broaden the team's depth, and the fact the Matildas have struggled to develop a discernible style to match it with the world's best.
Gustavsson did not relocate to Australia during his tenure as Matildas boss and it is yet to be seen if FA will make that a prerequisite for any of his prospective replacements.
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