Manager Neil Lennon's second signing of the summer was subject to a work permit and has an option for a third year, Celtic said on their website.
The 29-year-old Cha, who played in three of South Korea's World Cup games before they were knocked out by Uruguay in the last 16, has been dubbed 'human weapon' for his habit of injuring opponents, team mates and coaches in training sessions and games.
Cha moves to Scotland after playing for Freiburg in Germany last season. Celtic, Scottish champions 42 times, had a disappointing 2009-10 season and finished six points behind city rivals Rangers.
"I am excited about playing for Celtic and living in Glasgow," the BBC quoted him as saying.
"Celtic are a big club and have a good chance of winning trophies and I really want to play in a Glasgow derby," added the converted forward.
"Even in Germany, people talk about the Old Firm game, so to actually play in one would be amazing."
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