At international level, he was part of England's squad at the 2014 World Cup and 2016 UEFA European Championship, and featured for Team Great Britain at the 2012 Olympics in London.
He made the last of his 27 senior appearances for England in 2017.
Sturridge, 32, left Turkish side Trabzonspor in March last year, after being handed a four-month worldwide ban for breaching betting rules.
He is alleged to have instructed his brother Leon to bet on a possible move to Spanish club Sevilla during the Jan. 2018 transfer window.
The move didn't eventuate, but an independent commission found Sturridge guilty of breaching betting rules.
He was handed a six-week ban, with four weeks suspended, but that was increased to four months after a successful appeal by the Football Association.
Sturridge has not played for a professional side in 18 months, and is excited to begin a new chapter at the Glory.
"It's a fantastic opportunity to try a new challenge," he said.
"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 [to] help the team be as successful as they possibly can be.
"I'm going to put my best foot forward, work hard and try [to] help the team win each game that comes by, and then we'll see where we end up when the season finishes."
Sturridge, who got his first big break at Manchester City, is one of the most high-profile players to ever sign for an A-League Men's club.
Others include Italian great Alessandro Del Piero (Sydney FC), Dwight Yorke (Sydney FC), Robbie Fowler (North Queensland Fury and Perth), William Gallas (Perth), Harry Kewell (Melbourne Victory and Melbourne Heart), Tim Cahill (Melbourne City), Keisuke Honda (Melbourne Victory) and David Villa (Melbourne City).
"Daniel is undoubtedly one of the biggest signings not only in Glory's history, but in the history of the A-League," Glory owner Tony Sage said.
"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."