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.

The new Manchester City striker headed the Elephants in front from a right-wing cross by Max Gradel.
Hilal Soudani equalised for Algeria against the run of play early in the second half and then forced goalkeeper Sylvain Gbohouo into a brilliant save.
Gbohouo was rewarded when Bony headed in Yaya Toure's free-kick and Junior Tallo set up Gervinho for a late third.
The margin of victory flattered Ivory Coast in what was an even contest and before former Arsenal striker Gervinho confirmed the result on the break, they had been under pressure from Algeria.
Their defence seemed all over the place at times and semi-final opponents DR Congo will have taken note.
Algeria, in the quarter-finals for the first time since 2010, made the brighter start to the contest and almost went ahead in the ninth minute.
Yacine Brahimi raced into the left-hand side of the penalty area and the Elephants' defence failed to deal with his cross, allowing Soudani to get in a shot which was well held by Gbohouo.
In the 21st minute, Riyad Mahrez volleyed over from close range but then Ivory Coast hit back.
Two minutes later, Gradel floated in a free-kick from the left and Serge Aurier's downward header hit the base of the post and then in the 26th minute they took the lead.
Gradel was again involved as he delivered a testing cross from the right and Bony escaped the defence to head home from eight yards.
Bony shot wide from distance towards the end of the first half before at the other end, Saphir Taider's sharp volley was confidently saved by Gbohouo.
The start of the second half mirrored the start of the first with one team dominating but the other one scoring.
This time Ivory Coast were the team who started on top but a comedy of errors in their defence after a deep cross into their penalty area finally saw the ball fall to Soudani, who fired it home.
That sparked a spell of dominance from the Desert Foxes with Gbohouo twice having to clear his lines before he made an amazing 66th minute save from Soudani's point-blank effort.
The momentum changed and two minutes later Bony restored Ivory Coast's lead when he climbed highest to head Yaya Toure's set-piece inside the near post.
Algeria piled on the pressure in the closing stages but could not find an equaliser and Gervinho finished them off when he passed the ball into the net.
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.
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Wilfried Bony scored twice to take Ivory Coast into the semi-finals of the Africa Cup of Nations.