The 24-year-old hadn’t competed since the team final last week in which she performed on the vault before saying she wanted to protect her mental health and withdrawing from the remainder of the event.
Biles said she was struggling with “the twisties”, which gymnasts describe as a sort of mental block, and she pulled out of the all-aroun, vault, floor, and uneven bars events.
She returned to action on the final day of artistic gymnastics to a warm reception at the Ariake Gymnastics Centre and scored 14.000 with a solid showing ending in a double backward somersault and double pike onto the mat.
She jumped up and down in celebration, embracing her rivals at the end, and said afterwards that she hadn’t been expecting a medal.
"I just wanted to go out there for me and that's what I did. I was proud of myself just to go out there after what I've been through,” she added.
China' s Guan Chenchen won gold with a total score of 14.633 with compatriot Tang Xijing scoring 14.233 to take the silver.
It was a seventh Olympic medal for Biles, who went third out of the eight finalists, making her the joint-most decorated American gymnast in history alongside Shannon Miller and her second of Tokyo 2020 after the USA won silver in the women’s team final.
After the event the Texan athlete insisted that making her return to the competition was about more than just a podium appearance.
Biles continued: “It definitely feels a little bit sweeter than my 2016 bronze medal.
"In the other events I physically couldn't twist in the air, I would just keep crashing and I just wasn't cleared safely to do those things.
"I pulled out of my other finals just because I wasn't clear to do them. I didn't think I was going to be clear to beam, it just means the world that I can come out here and compete one more time before this Games is over."