City confirmed the deal for the 22 year-old centre back who will move to the South Korean club for an undisclosed fee.
Chapman completed his medical with Incheon United yesterday and will leave South Korea on Tuesday to link up with his new team-mates at a training camp in Thailand.
"I'm happy to join a big club in the K League - Incheon United," Chapman said in a statement.
"I know that Incheon is one of the most beautiful cities in Korea. I'll do my best to show good performances here."
Chapman was the first signing of the City Group's takeover of Melbourne Heart in 2014
The 22-year-old departs City after 35 A-League games over two-and-a-half seasons having joined from Newcastle Jets in 2014.
The defender has recently struggled for match time after the emergence of Ruon Tongyik to make only five A-league appearances this season.
Chapman Joins fellow Australian Tomislav Mrcela in the K-League, who is on the books of Jeonnam Dragons, while former Sydney FC and Newcastle Jets midfielder Ali Abbas plays for Pohang Steelers.
