Atkin produced a clean final run to score 84.60 and move into third place. She then faced a nervous wait as the final three athletes took their last runs but the Briton held on to secure her medal.
The 19-year-old's name goes into the record books alongside that of snowboarder Jenny Jones as the only two Britons to have won medals on snow in the 94-year history of the Winter Games.
Jones won bronze in the snowboarding slopestyle at Sochi four years ago.
In 2002, British Alpine skier Alain Baxter won slalom bronze at the Salt Lake City Olympics but was stripped of the medal three weeks later after testing positive for a banned stimulant which he blamed on an over-the-counter cold remedy.
Atkin celebrated with friends and family who were gathered at the base of the slopestyle course to greet her.
“I am overwhelmed and excited. I can’t put my thoughts into words,” Atkin told reporters. “Jenny was really stoked for me. It has been amazing.”
Atkin, who won a world championship silver medal last year, was born in the United States and lives in Utah but has a British father.
She went to school at Park City’s Winter Sports High School, which also boasts gold medallists Ted Ligety, Julia Mancuso and Joss Christensen as alumni.
The teenager’s medal is Britain’s second of the Pyeongchang Games after Dom Parsons won bronze in the men’s skeleton on Friday.
(Editing by Clare Fallon)
