After becoming the third woman in history to win a second Olympic all-around title, Simone Biles wore a diamond-encrusted goat necklace during the medal ceremony.

Three years after withdrawing from the team final of the Tokyo Olympics because of a mental block, a move that prompted critics to call her a loser, a quitter and un-American, Simone Biles on Thursday proved to the world — and to herself — that she was unstoppable.

Wearing a leotard reminiscent of Wonder Woman’s suit, Biles, 27, won the all-around title at the Paris Games, becoming the oldest all-around champion since 1952 and only the third woman — and the first since 1968 — to win two Olympic all-around titles.

The gold was Biles’s ninth Olympic medal, pushing her record total of Olympic and world championship medals to 39 and reaffirming her standing as one of the best athletes of all time.

After Biles learned that she had won, she waved to a crowd that chanted “U-S-A! U-S-A!” and then walked off the raised platform, rested her elbows nearby and exhaled.

“All in all, I’m super proud of my performance tonight and the fight that I had for the last three years, mentally and physically, just to get back competing on a world stage, Olympic Games,” she said, adding, “I couldn’t be prouder.”

Except for an uncharacteristic mistake on the uneven bars, Biles nailed her routines and did so under extraordinary pressure, as Rebeca Andrade of Brazil was having a fantastic night. Andrade, the silver medalist in the all-around in Tokyo, had led the competition after the second of four events.

With Andrade battling her for the lead until the end, Biles said she had never been so stressed during a gymnastics meet.

“I don’t want to compete with Rebeca no more. I’m tired,” she said, as a joke. “She was way too close. I’ve never had an athlete that close, so it definitely put me on my toes and brought out the best athlete in myself.”

Andrade won the silver medal, finishing 1.199 points behind Biles’s total. Biles’s teammate Sunisa Lee, the all-around champion in Tokyo, won the bronze — a remarkable accomplishment, considering what she has endured. After being diagnosed less than two years ago with two kidney diseases that limited her training, Lee thought that she might never compete in gymnastics again. Her coach Jess Graba said that after she won the bronze, he told her, “I will always put my money on you because you always fight.”

Lee, 21, credited Biles with helping her get through the night because “we were both freaking out.”

She and Biles giggled as Lee described their discussion of the scores as the competition unfolded. Both were trying to figure out where they would place.

We were literally, like, calculating,” Lee said. “I was like, ‘I don’t even know how to do math in my head and she was like, ‘Me, either!’”

After Tokyo, Biles took time off, just as Lee did — but for different reasons. Biles began seeing a therapist every Thursday to help reset her body and her mind. With no expectations of winning medals, she returned to her sport so her story would have a different, and better, ending.

Biles went into the all-around with confidence. Winning a gold medal earlier in the week — in the team event — helped. With fans waving huge photos of her head and banners that said “Simone for President!” on them, she performed with both joy and genius as the Americans reclaimed the Olympic title. The American team won silver in Tokyo.

But on Thursday, the all-around was not so simple for Biles, who had become accustomed to winning by comfortable, if not cavernous, margins. Andrade, who finished second to Biles at last year’s world championships, put pressure on Biles with brilliant performances on each apparatus.

Biles started the competition on vault, which bedeviled her in Tokyo when she became disoriented in the air. Just as she did earlier in the week, Biles aced her dangerous vault, the Yurchenko double pike, which allows almost no margin of error: She could easily land on her head or break her neck.

On this night, there were no flashbacks. No anxiety. Just Biles, at 4-foot-8, flying like a radiant red, white and blue ball of fireworks, as the crowd hushed. When she landed on her feet, the spectators roared, applauding an effort that would earn her 15.766 points — an excellent score.

Next up were the uneven bars. An uncharacteristic break in her routine gave Biles a lower than usual score, allowing Andrade and Kaylia Nemour of Algeria to move ahead of her in the standings.

But Biles kept her composure, performing a solid routine on the balance beam, scoring 14.566 points to move into the lead, but only by 0.166 points. Andrade’s score on the beam moved her into second place.

“Knowing that I gave Simone a bit of work is cool, right?” Andrade said in Portuguese, with a laugh. “She’s the best in the world. Simone is a phenomenon.”

Knowing that I gave Simone a bit of work is cool, right?” Andrade said in Portuguese, with a laugh. “She’s the best in the world. Simone is a phenomenon.”

While Biles’s attitude at the Olympics had been super upbeat going into the all-around, smiling between events and joking with her teammates during the team final, it seemed to change as Thursday’s event unfolded. She was proud of herself for rediscovering her love for the sport and for returning to the Olympics, but she was also an intense competitor who wanted to win. Her smile disappeared, replaced by a fierce look of concentration.

Only the floor exercise was left. Biles had qualified first in the event, with Andrade in second. Biles went in with an edge: Her floor routine is the hardest in the world, with the highest degree of difficulty and the best chance for an enormous score.

Performing her routine to screams from the crowd and, initially, to the deep, loud beats of the song “…Ready for It?” by Taylor Swift, Biles hit complicated tumbling pass after complicated tumbling pass to score 15.066 points — and won.

After her score was posted, she put on a sparkly necklace in the shape of a goat, alluding to the acronym GOAT, for Greatest of All Time. But she is not done yet: She has three more chances for medals at the Paris Games and will compete in the finals of the vault, balance beam and floor exercise.

“I know people will go crazy over it,” she said of the necklace. “But at the end of the day, it is crazy that I am in the conversation of greatest of all athletes because I just still think I’m Simone Biles from Spring, Texas, that loves to flip.”