Split confirmed Lustica's departure on their website on Monday, saying the 22-year-old Australian was keen to continue his career in Australia.
Lustica struggled for game time at Split, sent out on loan to Dugopolje and Brisbane Roar after joining in June 2011.
Speaking at Adelaide's fan forum on Monday night, the South Australian club's football manager Michael Petrillo said the club would be announcing the signing of a European-based Australian in the next 24 hours.
"Steven is the type of player that fits with the football philosophy of the coach," Petrillo said.
"(Adelaide head coach) Josep (Gombau) has had a good look at several players and has opted for Steven because he is technically very good, believes he can adapt quickly to the style of play and has had A-League experience.
"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."
