The New Zealander finished in champion style with a superb birdie on the 18th hole of a windswept Old Course to complete a round of three-under-par 69 and claim her third major title with a tournament total of seven under.
"It is surreal," Ko told Sky Sports. "Winning the gold medal in Paris a few weeks ago was almost too good to be true. Heading into the weekend I thought 'how is it possible for me to win the Open?'.
"This is almost too good to be true. Out of all the major championships, this was the one I had the least amount of confidence in."
Victory gave Ko, 27, her first major since she won the 2016 Chevron Championship.
Ko, who as a 17-year-old became the youngest player to be ranked number one in professional golf, added: "It is the most Cinderella-like story these past two weeks. To be holding this trophy now, it is some achievement.
"I thought to myself because of the last few weeks it is not going to happen. So don't overreact and play the shot in front of you. My two goals were to par the 11th and birdie the 18th, I achieved both. This is such a special place.
"I always said I wanted to win another major championship. Here I am now as a three-time major champion."
Defending champion Lilia Vu failed to sink a 15-foot birdie putt on the last at the 'Home of Golf', to force a play-off and then missed from barely 12 inches as Ko, already in the clubhouse, completed a two-shot win.
Korda collapse
World number one Nelly Korda led by two strokes on the 14th tee of the renowned links course on Scotland's east coast following a run of three birdies in four holes around the turn.
But the American then took seven shots on the par-five 14th.
Her bid for victory finally ended when she found the infamous Road Hole bunker on the 17th, which she subsequently bogeyed.
Korda finished in joint-second place alongside Vu, Yin Ruoning and Shin Ji-yai on five under.
"I had 58-degree (for my third shot), and it just shot on me," Korda said of her double bogey on the 14th.
"The wedge shot I had over the green was sitting a little bit in a hole with some of 'hay' or whatever you call it behind it. I just couldn't catch it cleanly and then obviously didn't make the putt for bogey."
England's Charley Hull, who led after the first round to raise hopes of a first major title after finishing runner-up in both last year's Women's British Open and Women's US Open, endured a frustrating final day before she finished tied for 20th on one over par.
But compatriot Lottie Woad won the Smyth Salver, awarded to the tournament's leading amateur, after a closing birdie gave her a total of one-under par.