Henderson, who became the second youngest woman to win a major at the age of 18 and nine months, defeated World. No.1 Ko at Sahalee Country Club, Seattle, on the first extra hole of the playoff.
Ko, who won last year's Evian Championship aged 18 years and four months, had led going into the final round with the New Zealander aiming for a third consecutive major title
but she was unable to cope with her opponent's late charge.
It caps a remarkable year for Henderson, who began 2015 ranked 221st in the world and is now set to move up to second in the rankings with the pinnacle very much in sight.
"To become world No. 1 you have to compete every week and have a lot of wins," Henderson told reporters.
"This is only my second win on the tour, but I've had a lot of top five finishes or top 10 finishes.
"I''m looking forward to the rest of the summer. There are still three major championships left and I'd like to get my name on all three of those, but I might be getting ahead of myself."
Canada's Henderson carded a six-under 65 including a staggering eagle putt on the 11th before moving level with Ko, who finished with a final round of 67.
She then claimed the $525,000 first prize by sinking a three-foot putt at the first extra hole to stun Ko and secure her maiden major title.
Henderson is just the second Canadian to win a women's major, following Sandra Post who won the Women's PGA Championship in 1968.
"The last couple of days the support for Canada has been really incredible," Henderson said.
"Walking down the fairway they were yelling my name. But last time they were just yelling 'Go Canada' and that was kind of a surreal feeling.
"I can't really put words to it. But I'd like to say that I am the Canadian face to women's golf and I'd like to say I'm a good athlete for Canada."