The current world number one sealed the deal in one hour and eight minutes as she beat the 18-year-old American 6-1 6-3.
Swiatek extended her winning run to 35 games - the longest since Venus Williams' 35-match streak in 2000 - and pocketed €2.2million along the way.
Gauff, who was making her first appearance in a major final, got off to a nervous start as she handed her opponent an early break with a double fault.
Swiatek capitalised on every mistake and utilised her enormous forehand to claim the opening set with relative ease.
Gauff put on a better display in the start of the second set, but the teenager was unable to keep up the resistance for long.
Instead, it was the world number one who showed her class by storming her way to a second French Open crown.
Speaking after the match, Swiatek praised her opponent, saying: "First of all, I want to congratulate you, you're doing an amazing job. I can see that every month, you're progressing every time.
"When I was your age I had my first year on tour and I had no idea what I was doing. You will find it and you will be there, I'm pretty sure of that."
Swiatek went on to credit her team, adding: "I want to thank my team. Without you I wouldn't be here, I'm sure of that. I'm pretty happy that every piece has finally come together and we can do this because I feel like you are working hard, I am working hard and we all deserve to be here. Thank you guys for full support.
"Two years ago, winning this title was something amazing. Honestly I couldn't expect it ever, but this time I feel like I worked hard and did everything to get here even though it was pretty tough. The pressure was big so thank you to all the fans for coming."
A tearful Gauff reflected on a chastening first experience of a major final.
"Congratulations Iga, what you have done these past few months has been amazing," she said.
"Hopefully we can play many finals and I can get a win on you one of these days.
"I'd like to thank my team. I'm sorry I wasn't able to get this one today."