The 31-year-old Gordon, capped 40 times by Scotland, has not played professionally for two seasons following his release from Sunderland in 2012 after a series of arm and knee injuries derailed his career. But he will have the chance to resurrect his career at Celtic Park, where he will provide competition to incumbent first-choice keeper and England international Fraser Forster.
"I want to play as many games as I possibly can," Gordon said. "I have not been told anything (about whether I will be first or second choice) and I've not asked anything. For me to be here at all is an achievement. It's a fantastic club to be joining after the injury nightmare I have had.
"I'm grateful to have this opportunity and I'm going to work as hard as I possibly can to play as many games as I can. I came close to the point where I thought I might never play again. I had to work very hard and put in a lot of hours that will hopefully stand me in good stead once I get back into full training and playing games."
Gordon was set to fly out to Austria later on Thursday to join up with coach Ronny Deila and his team-mates at their pre-season training camp.
Edinburgh-born Gordon started his career with Hearts, winning the 2006 Scottish Cup with his hometown club, before earning a £9m move to Sunderland in 2007, then a British record fee for a 'keeper.
However, his time at the Stadium of Light was blighted by a series of injuries before he lost his place to Simon Mignolet, now at Liverpool, ahead of the 2010/11 season with further knee problems eventually spelling the end of his time with the Black Cats.