The pick came as little surprise after Clark toppled the all-time NCAA scoring record and sent TV ratings soaring during the March Madness tournament in her final college season.
"I'm just very lucky to be in this moment and all these opportunities and these things are once in a lifetime," said Clark.
Fans swarmed outside the Brooklyn Academy of Music and a sold-out crowd cheered wildly as Commissioner Cathy Engelbert announced Clark's selection.
Stanford's fearsome shot-blocker Cameron Brink went second to the Los Angeles Sparks, and the Chicago Sky took South Carolina's Brazilian phenom Kamilla Cardoso third.
More than 18 million tuned in to watch South Carolina thwart Iowa in the collegiate finale last week. Clark will be one of the biggest attractions in the upcoming WNBA season, and the ticket resale market has surged in anticipation of her arrival.
"We are witnessing a transformational moment in sports that we may not experience for generations," Engelbert told reporters ahead of the draft on Monday night. "We are ready for this moment."
Clark joins last year's first overall draft pick and unanimous Rookie of the Year, Aliyah Boston, at an ailing Indiana Fever franchise that has not enjoyed a winning season since 2015.
"I am confident she will have an immediate impact on our team and the league," Fever General Manager Lin Dunn said in a statement. "Any time you can add two consecutive No. 1 draft selections, it creates enormous interest and visibility."
Clark said she would lean on Boston and some of the team's more senior members as she navigates a new chapter in her career.
"I'm 22 years old, and, I don't have all the answers in the world," Clark told reporters. "This is something new to me. This is a new challenge. And that's something I'm excited for."
The WNBA regular season begins on May 14.
