Gallas has agreed to terms for a one-year deal, with the contract to be finalised after he undergoes a medical examination in the coming weeks.
The former French international has been on the lookout for a new club after being released by English Premier League side Tottenham Hotspur at the end of last season.
EPL clubs Crystal Palace and Manchester City had shown interest in signing Gallas, along with outfits in the Middle East and America.
Melbourne Victory were also said to be interested in Gallas.
The addition of Gallas is a huge boost to the A-League, which is still riding a wave of momentum following last year's arrivals of veteran trio Alessandro Del Piero, Shinji Ono and Emile Heskey.
Perth Glory hope Gallas' arrival will help spark renewed interest in the club, which has struggled to regularly attract big crowds since the inception of the A-League.
Gallas, who appeared in two World Cups, two European Championships and won back-to-back English Premier League titles with Chelsea, will become the first Frenchman ever to play in the A-League.
"I hope to help my new team mates and club achieve success in this season and hope to help deliver to the fans of Perth the championship they are looking for," Gallas said in a statement.
"I look forward to this new challenge and hope to excite the fans."
Glory coach Alistair Edwards was thrilled to add a player of Gallas' experience to his youthful side.
"What better player in world football to bring to Western Australia than someone with 84 caps for one of the best footballing nations in the world?" Edwards said.
"He has played alongside some of the best players in world football and worked under some of the most decorated managers and coaches of all time, including Arsene Wenger and Jose Mourinho, people whom I have the utmost respect for.
"Gallas fits into our vision of providing the best environment for our youth to flourish.
"He knows that he is coming into a wonderful culture built around great experienced players and some of the most talented young players in Australian football."
The ninth-placed Glory will play their first home game of the season on Sunday when they host Melbourne Heart at nib Stadium.
Defender Josh Risdon will miss the clash with a knee injury, while star striker Shane Smeltz is still recovering from a hip operation.