The Government says it loses about $500,000 a year managing the soccer ground through the Office of Recreation and Sport.
Sports Minister Tom Kenyon says the Entertainment Centre, which is state-owned but operates autonomously, is confident it can turn a profit from the stadium.
Mr Kenyon says hosting concerts at the stadium is one option for the new managers.
"You'd have a whole precinct, a whole entertainment precinct down there at Hindmarsh run by one manager of events and they could use it to run bigger concerts there," he said.
"A summer evening concert could be a good thing."
Mr Kenyon says the Government has been looking to transfer the stadium's management for some time and the deal will benefit taxpayers.
"Stadiums are expensive. It's hard to make them profitable and they need a lot of maintenance," he said.
"We've always known it's not the best way to run it. It's a matter of coming to an arrangement that works for everybody."
Mr Kenyon says the change in management will not affect the deal with the stadium's major tenant, A-League club Adelaide United.
"It'll continue to be available for them," he said.
"They also have the best deal in the country, the best stadium deal in the country by a long way and we have assurances from the Adelaide Entertainment Centre that will continue."
The Government says it will give up its corporate suite at the stadium.