The former Juventus and Bayern Munich star was halfway through a two-year deal with Sydney, but it has been announced the contract has been ripped up.
Both parties agreed to the termination with Costa needing to address personal and business issues at home in Brazil.
Last season, Costa made 25 appearances, scoring six goals and registering eight assists.
A statement from the A-League club read: "Sydney FC has terminated the contract of Douglas Costa by mutual consent, with the winger unable to travel to Australia.
"Ongoing legal and personal matters in his home country have prevented the Brazilian from leaving.
"Thanks for your efforts in Sky Blue, DC".
Costa himself added: "I am very sorry that I cannot return at this time due to the matters I must resolve at home, but I will always remember my time in Sydney fondly.
“I want to thank Sydney FC for giving me the opportunity to play in Australia. It was an incredible year in Sky Blue.
“To the members and fans, I truly appreciate the support you gave me and the team. Playing in front of you was very special, and I will never forget it.”