Costa, who won a slew of trophies with Bayern Munich and Juventus, will arrive at the five-times A-League champions following a difficult term with Fluminense in Brazil's top flight.
Costa failed to score in 22 appearances for the Rio de Janeiro club where he landed in January after Juventus ignored his appeals to return to the Italian giants.
Prior to Fluminense, Costa had a lucrative but troubled two-season stint at Major League Soccer side LA Galaxy where he was blighted by injuries and off-field legal problems.
Though Costa's best days are likely behind him, Sydney FC hailed his signing as a "massive coup" for the club and for Australia's struggling professional league which has slashed funding to clubs to cover mounting losses in recent years.
"He is one of the most high-profile footballers to ever play on these shores and the eyes of the football world will be on Sydney FC and the A-League this season," Sydney FC Chairman Scott Barlow said in a media release on Monday.
With more than 13 million social media followers, Sydney will hope for more than just goals and assists from their new marquee player.
"Only Australian sports stars such as cricketer David Warner and Formula 1 driver Daniel Riccardo (have) a comparable online status," the club said.
Costa will arrive in Sydney this week and play his first game on September 19th against Hong Kong team Eastern FC in the AFC Asian Champions League 2 competition.
"I have been part of some incredible teams throughout my career, winning many titles and I have come to Sydney FC to win more," said Costa, who made the last of his 31 appearances for Brazil in 2018.
"Football is in my blood and I arrive in Australia to raise the game in this country, entertain the passionate sporting public and bring silverware to Sydney FC."
