"Hopefully this is the first of many [majors] to come. It was my time."
The victory meant Ochoa became the first player to win their first major title at St Andrews since Tony Lema at the men's British Open in 1964.
Ochoa had led the tournament from the ninth hole of the opening round. She then began the final round with a six-stroke lead and the only player under par.
The only player to master the winds on the course, her only hiccup came when she bogeyed the 17th, but by then her name was on the trophy.
She went to the last hole four shots ahead and a par captured the title.
Again it was her approach shots which put her in complete control.
Birdies at the fifth and sixth holes put her at 8 under. Despite three-putting at the eighth, she made a 25-foot birdie putt at the ninth to reach the turn in 34, 2 under for the day.
From that point, the championship was all but all over.
Ochoa lines up her putt on the 18th green [GALLO/GETTY]

Her rivals simply failed to make Ochoa pay for any of her mistakes.
Although she missed a 4-foot par putt at 11, her lead stayed at five because playing partner Linda Wessberg also dropped a shot.
The Swede dropped out of contention with a 7 at the par-5 14th after her drive went out of bounds.
At one point 3 under, Wessberg finished with a 75 for a 2-over 294.
Former world number one Annika Sorenstam, who started the day tied for third going into the final round, also failed in her chase on the final day after hinting at a challenge with two birdies in the first six holes.
But the charge vanished with three bogeys in the next five and her wayward drive at 17 for a 7 left sliding down the board. The 10 time major champion finished tied for 16th at 4 over after a 76 that included a 7 at the 17th Road Hole.
"Everybody knows she is a fantastic player," Sorenstam said.
"She's had a great run the last year and a half. She has matured a lot as a player.
"I think a major was just a matter of time. I'm very happy for her. She is a great person and a great player."