The 22-year-old struggled for game time at Split, sent out on loan to Dugopolje and Brisbane Roar after joining in June 2011.
Split confirmed Lustica's departure on their website on Monday, saying he was keen to continue his career in Australia.
According to Croatian daily newspaper Slobodna Dalmacija, Adelaide were keen to lure the former Young Socceroo to Coopers Stadium.
"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 the newspaper.
"Tudor was my idol...but my career has to go forward. I'm hoping to play at the World Cup in Brazil."
At Adelaide's fan forum on Monday night, Reds football manager Michael Petrillo said the club would be announcing a signing in the next 24 hours and this morning the club confirmed Lustica's arrival.
The former National Youth League Player of the Year when he was representing the now defunct Gold Coast United, Lustica was snapped up by Hajduk Split during which time he competed in the UEFA Champions League for the Croatian giants against the likes of Arsenal and FC Barcelona.
“Steven is the type of player that fits with the football philosophy of the coach,” Adelaide United General Manager – Football Operations, Michael Petrillo said.
“Josep 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.”
Lustica will arrive in Adelaide on the weekend.