The world number two is 18 years, four months and 20 days old.
The previous record was held by American Morgan Pressel, who was 18 years, 10 months and nine days old when she won the Kraft Nabisco in 2007.
Ko shot eight birdies in a final round of 63 to finish on 16 under par, with American Lexi Thompson on 10 under.
In February, aged 17, Ko became the youngest player to reach the top of the rankings and she also holds the record as the youngest winner on the LPGA Tour after her Canadian Open victory as a 15-year-old amateur in 2012.
It was Ko's last opportunity to beat the age record as she would have been too old by the next major, the ANA Inspiration, in April.
"It has been such an unbelievable experience," Ko told Sky Sports. "Now everybody won't ask me when I will win my first major because it is done.
"It is definitely one of the top rounds of my whole life."
Ko had started the day in third place, two shots behind overnight leader Lee Mi-hyang of South Korea.
Tournament organisers decide to use split tees, using the first and the 10th, due to the threat of thunderstorms on Sunday afternoon.
Lee's challenge faded and she finished tied for fourth place, nine shots behind Ko, after carding a three over par 74.
England's Charley Hull was six over for the day and finished tied for 38th place, while Republic of Ireland amateur Leona Maguire was tied for 34th.
New Zealand's Lydia Ko has become the youngest winner of a major with a six-stroke victory at the Evian Championship in France on Sunday.