It's the first major and sixth career LPGA Tour victory for the 24-year-old South Korean star, who came into the tournament ranked fifth in the world.
Choi shot 1-over-par 73 on Sunday and finished at 7-under for a four-stroke victory. Fellow South Korean player Amy Yang had 71 to finish second.
Choi came into Sunday with a six-stroke lead after shooting 7-under 65 on Saturday. She got into trouble when she triple-bogeyed No. 10, but recovered to win at the same course where Se Ri Pak won South Korea's first major title in 1998.
Pak was among a group of friends who met Choi after she putted out on the 18th green, showering her with hugs <0x2014> and victory champagne.
Choi becomes the fourth South Korea player to win the event in the five years, following Inbee Park (2008), Eun-Hee Ji (2009) and So Yeon Ryu (2011).
Choi and Yang were the only players to finish the tournament under par.
Sandra Gal, of Germany, shot 74 and finished 1-over for the tournament. Il Hee Lee, of South Korea, Shanshan Feng, of China, and Italian Giulia Sergas finished 2-over.
Michelle Wie finished the tournament 10-over. After shooting 66 on Friday to close with a stroke of the lead, she had weekend rounds of 78 and 80.
Top-ranked Yani Tseng finished 14-over, and still needs an Open victory to complete a career Grand Slam.