The 18-year-old from Ehime, Japan, shot a final-round 67 to finish five shots ahead of Australia's Tarquin MacManus.
Both players earn exemptions into the British Open's international final qualifying field.
Matsuyama emerged from a 118-man field, made up of competitors representing 27 different Asia Pacific Golf Confederation member nations, to claim the crown.
Japan's Yosuke Asaji finished alone in third place, five strokes ahead of Korea's Lee Kyung-hoon and Ben Campbell of New Zealand.
Matsuyama made four birdies against no bogeys on the 7,068-yard West Course at Kasumigaseki Country Club.
"I'm very, very happy. I was under par for all four days and now I'm in the Masters, so that's very exciting," said Matsuyama, who reached 15-under with rounds of 68, 69, 65 and 67. "I was extremely pleased to keep the bogeys off my card today.
"It's harder to not make mistakes than to make birdies."
Matsuyama will become the first Japanese amateur to play in the Masters.