Carlsen defeated defending champion Viswanathan Anand of India after a draw in Game 10 gave him the necessary 6½ points to clinch the win.
Playing in Chennai close to where Anand grew up, the Indian finished with 3½ points after seven draws and three losses.
Carlsen becomes the youngest world champion since Garry Kasparov, who was also 22 when he won the title in 1985.
Carlsen is a former child prodigy who became a grandmaster at 13 and has been the world's top-ranked player since 2010.
The 43-year-old Anand had held the world title since 2007.
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