The 19-year-old, who finished second alongside Rory McIlroy at last week's Korea Open, fired a closing 70 for a three-under-par total to finish three shots ahead of Japan's Shohei Hasegawa.
"Playing in the Masters has been my dream since I started playing golf," said Lee, who won the Dongbu Promi Open on the Korean Tour last month. "I didn't think I would have an opportunity, so this is a great honour. I have never been so excited.
"I can't believe I am going to go to the Masters. I think I will only realise it tomorrow."
Defending champion Guan Tianlang, who made the cut at Augusta despite being handed a one-shot penalty for slow play in the second round, finished in a share of eighth place.
"It's been a pretty amazing year for me," said the 15-year-old, who was 14 and the youngest ever Masters competitor in April. "I didn't defend my title this week, although I felt like my game was good, but I really appreciate the opportunities the tournament has given me."