Sturridge had been without a club since he was let go by Turkish side Trabzonspor in March 2020 on the back of a four-month ban for betting-related offenses.
The 32-year-old, who has also enjoyed loan spells at Bolton Wanderers and West Bromwich Albion in the past, boasts 76 goals in 218 Premier League appearances.
He won the Champions League at both Chelsea and Liverpool, and has scored eight goals in 26 caps for England.
"It’s a fantastic opportunity to try a new challenge," Sturridge said in a statement posted to the club's official website.
"When the opportunity came about, it felt like the right thing to do, to take my talent somewhere where I can enjoy my football in a competitive league and try and help the team be as successful as they possibly can be.
"I’m going to put my best foot forward, work hard and try and help the team win each game that comes by and then we’ll see where we end up when the season finishes.
"I can’t wait to play at HBF Park and hopefully put a smile on a lot of faces."
Chairman Tony Sage added: "Daniel is undoubtedly one of the biggest signings not only in Glory’s history, but in the history of the A-League.
"His arrival signals in no uncertain terms how determined we are to bring sustained success to the club and the lengths we will go to in order to achieve that goal.
"We know the elite-level quality Daniel will bring to the side and are hugely excited to see him wearing the famous purple this season."
