Elsey, who is out for the season after tearing his anterior cruciate ligament, is a product of Adelaide's youth program.
"I saw enough of Jordan before his injury to know that he is a player that we look for in our centre-back positions – he can pass the ball and play from the back," coach Josep Gombau said.
"He has had a tough year with injuries and as soon as possible we want to get him playing as many minutes as he can so he will be ready for the new season."
Elsey made headlines last January with a thumping header to secure a memorable 2-1 win against Brisbane Roar, and the 20-year-old said he was looking forward to returning to action next season.
"I am happy to stay in Adelaide because of the playing style and it is also my home with so much support from the staff and players here," Elsey said.
"I can see the club going places with our style and this is where I want to stay and improve my game.
"My first priority is to look after my knee and the plan is that I will be ready for pre-season leading into the 2015-2016 campaign."
