The 29-year-old started the last day with a three-shot lead and she finished on 14 under par after a near-perfect closing 68.
Brooke Henderson, last year's winner, was second on eight under after a 70.
Boutier is the third French woman to win a major, following in the footsteps of Catherine Lacoste, who won the 1967 US Women's Open as an amateur, and Patricia Meunier Lebouc, a winner of the Kraft Nabisco Championship in California 20 years ago.
In ideal conditions, Boutier, a former world number one amateur, swiped away the nerves with a brilliant start. She birdied the first from ten feet and holed a monster putt for a two at the short second.
She sank another long birdie putt at the short fifth and, with all her challengers faltering, the lead had been stretched to six by the sixth and the record crowds were already preparing to salute a new star.
A first bogey of the day at the 13th saw the lead cut to four shots, but a birdie at the long 15th restored order and she could enjoy the walk down the 18th.
Canada's Henderson put up a stout defence but never really threatened to win and Japan's Nasa Hataoka, second overnight, slipped to joint third on seven under after
Boutier is already the most decorated French player on the LPGA Tour with three wins - including the Drive On Championship in March - and the two-time Solheim Cup player has already tasted victory on home soil at the 2021 French Open.
