"First of all, I'm not very good at speeches, and I won my last title, like, two years ago," Swiatek said after the match.
"I don't know what is going on. I am so happy. And I am so glad that my family was here, finally. I don't know, it's crazy.
"It feels like such a short time. So yeah, I'm just overwhelmed. Thank you all for cheering. It was an amazing final."
With a handful of spectators watching on, Kenin and Swiatek made their way onto Court Philippe-Chatrier to polite applause.
Moments after the match had started, viewers were complaining about a heavy shadow which was splitting the court in half.
Many were concerned the players would get distracted by the shadow of fluttering flags in the middle of the court.
The Polish teen started the contest by holding at love, and followed up by breaking serve and taking an early 2-0 lead.
Swiatek's powerful backhand proved a valuable asset during the opening passages of the match, the 19-year-old rarely making an error on the clay.
After winning 12 of the first 15 points in the match, Swiatek held serve to go 3-0 after just eight minutes.
New York Times tennis correspondent Christopher Clarey tweeted: "Iga Swiatek playing her first Grand Slam final like she's playing a practice match against a hitting partner."
Kenin finally got on the board in her second service game, before breaking Swiatek's serve in a dramatic shift in momentum.
With scores locked at 3-3 in the first set, the American had landed 78 per cent of her first serves in, while Swiatek had only managed 50 per cent.
The seventh game went to deuce twice, but Swiatek managed to hold serve with a few well-directed drop shots, despite another double fault creeping into her game.
But Swiatek then managed to break serve once again to secure a 5-3 advantage with her serve to come.
The 19-year-old botched a set point at 40-30, and Kenin kept herself in the contest by winning the next three points and bringing the set back on serve.
But Swiatek rallied to secure another two set points in the following game, and broke serve to ensure she was one set away from a maiden grand slam title.
Radio presenter Lexis Bill tweeted: "You'd have thought the French Open finals will be a walk in the park for Sofia Kenin but Swiatek is mean! What a game they're serving us."
Tennis journalist Ben Rothenberg posted: "This final is already much, MUCH better than last year's French Open women's final, which was an all-time dud."
As she has done throughout the tournament, Kenin took a lengthy break after losing the opening set.
But when play resumed in Paris, both competitors played a dynamic brand of tennis, each delivering several powerful winners.
Kenin immediately broke serve to get her second set off to a flyer, but the relentless Swiatek managed to do the same from the other end, bringing the set back on serve.
The American became agitated as the match progressed, sporadically yelling, shaking her head and throwing her arms in the air.
Kenin was spotted kicking her racquet, and her father was also heard yelling at the Australian Open champion from the stands.
New York Times tennis correspondent Christopher Clarey tweeted: "Kenin's go-to shot, her backhand, is breaking down more than usual today. Perhaps a combo of final pressure and heavy Swiatek groundstrokes but it's got to change if Kenin is going to push this match into a third."
After consulting a medic about her heavily-strapped thigh, Kenin briefly left the court at 2-1in the second set for a medical time out.
The three-minute break didn't help Kenin, who conceded a 3-1 lead when Swiatek quickly broke serve.
Continuing that momentum, the Polish teen then held serve at love, and was suddenly just two games away from a maiden French Open title.
Swiatek then broke serve once again — the game only lasting about two minutes — and the result seemed inevitable.
A few minutes later, a forehand winner secured Swiatek's maiden grand slam singles title.
After the final point, Kenin sat by herself in tears on the court as Swiatek celebrated the historic victory with her family.
"I just want to congratulate eager and a great tournament, a great match. You played really well. Congratulations to you and your team," Kenin said after the match.
"I would like to thank the crowd. It is finally good to see you guys with his whole pandemic. So thank you so much for your support and supporting me these past weeks. It really means a lot."
As Swiatek lifted the Suzanne-Lenglen Cup, the Polish national anthem blared around the stadium, the first time ever at a grand slam final.
