According to the club, the termination was decided by mutual agreement "as the winger was unable to travel" to Sydney.
The winger was reportedly arrested in Rio Grande do Sul for failing to pay child support, and is now prohibited from leaving Brazil.
"Despite being given more than two months to resolve these issues, Douglas Costa has informed Sydney FC that there is no forecast for them to be resolved," the club statement said.
"We have supported him over the last two months in trying to resolve his issues, but we agree that this is the best way forward."
"I very much regret not being able to return at this time due to issues that I need to resolve at home," said the 35-year-old striker, now free on the market.
Formerly of Juventus and Bayern Munich, Douglas joined Sydney FC in August 2024 after leaving Fluminense.