The 22-year old midfielder, who joined Hajduk from Gold Coast United in 2011, underwent loan spells with NK Dugopolje and Brisbane Roar over the past two years but has returned to Australia to sign a one-year deal with the Reds.
"I'm happy to have played for Hajduk and that I have been trained by the likes of (Goran) Vucevic, (Ante) Mise, (Krasimir) Balakov, (Miso) Krsticevic, (Igor) Tudor," Lustica told Croatian daily newspaper Slobodna Dalmacija.
"Tudor was my idol...but my career has to go forward. I'm hoping to play at the World Cup in Brazil."
Adelaide general manager Michael Petrillo added: “Steven is the type of player that fits with the football philosophy of the coach.
"He has also spent several years in Europe at a very good club like Hajduk Split where he played in the UEFA Champions League as well. Steven will add versatility to our midfield and at just 22 years of age we believe he has a bright future ahead of him.”