The 21-year-old striker joins from K League 1 club Suwon Samsung Bluewing for £2.5 million ($3 million).
Oh, who has one cap for his country, scored 14 goals in 53 games for Suwon.
He joins Celtic’s collection of Asian talent with six Japanese players having followed manager Ange Postecoglou from the J-League to Scotland over the past two years.
“He is a young and talented striker with great attributes who is ready to take the next stage of his career,” Postecoglou told the Celtic website.
“I’ve watched Oh for a while now and he’s a striker I really wanted because I think he’ll fit in really well in our team.
“It’s really important, I know he also put his heart into joining us and his tenacity has been crucial in getting this deal done.”
Oh will sign a five-year deal with the Hoops subject to international clearance.
He is expected to replace Giorgos Giakoumakis with the Greek international as he nears a move to MLS side Atlanta United.
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