Biles, who famously withdrew from multiple events at the Tokyo Games three years ago with the disorientating "twisties", followed up her team gold with the United States earlier this week. Defending Olympic champion Sunisa Lee took bronze.
The 27-year-old Biles became the first gymnast to reclaim the individual title, which she won at the 2016 Rio de Janeiro Games.
She capped her performance with another electrifying floor routine to Taylor Swift's hit song "Ready for It", her high-flying tumbling bringing the crowd to its feet.
She scored 59.131 points to finish 1.199 ahead of Andrade with 21-year-old Lee sealing bronze with her floor routine, having trailed in fourth going into the final rotation.
It was the first time that two women's Olympic all-around champions have gone head-to-head chasing a second crown.
The United States have now won the event six times in a row -- and a record seven times overall.
Biles has won nine Olympic medals including six golds, and donned a silver necklace of a goat after her performance -- a nod to her being considered the greatest gymnast of all time.
"My GOAT necklace - some people love it, some people hate it," said Biles.
"It is crazy I'm in the conversation of greatest of all athletes because I'm just Simone Biles from Spring in Texas.
"Three years ago I never thought I'd step on a gymnastic court again, but worked hard, mentally and physically, even saw my therapist this morning, just making sure I'm mentally well."
She could add three more golds in Paris as she competes in the apparatus finals on the vault, floor exercise and balance beam.
Stars turn out
Once again the stars were out for Biles, with Team USA basketball stars Kevin Durant and Stephen Curry watching at Bercy Arena along with NBA legend Tony Parker, footballing great Zinedine Zidane and American model Kendall Jenner.
On her first rotation, Biles opened with her stunning Yurchenko double pike vault -- now known as the Biles II -- earning 15.766 despite a big step back, to the delight of the crowd.
She pulled 0.666 points ahead of Olympic vault champion Andrade, who scored 15.100 for her perfectly-executed but technically less difficult Cheng.
Lee was trailing down in a distant seventh.
But Biles dropped to third after her second rotation on uneven bars, scoring 13.733 after an error on her weakest apparatus, allowing Andrade to move 0.267 ahead of the American after tallying a mark of 14.666.
Algeria's Kaylia Nemour lifted herself into contention after a terrific uneven bars routine, scoring 15.533, to move into second with Lee in fifth at the halfway point.
But Biles was back in front after the balance beam, finishing with a massive smile and high-fiving her teammates and coaches as she received a standing ovation for an effort worth 14.566.
She had a slim margin of 0.166 on Andrade, who had a few wobbles on the beam, with all to play for heading into the floor routine finale.
Biles finished with a flourish on the floor where she won Olympic gold in 2016, drawing gasps from the crowd with her gravity-defying jumps including two of her own skills.
Andrade, 25, knew she had been well beaten and the Brazilian, the Tokyo silver medallist, went over to congratulate and hug her rival even before the winning score of 15.066 flashed up.
For Andrade it was a second silver in Paris after helping Brazil to their first Olympic team medal.
Biles has returned to the Olympic stage stronger than ever after making her comeback in August last year following a two-year break, winning four gold medals at the world championships in Antwerp.
She becomes the third woman to win two Olympic all-around gold after Larisa Latynina of the Soviet Union and Czech Vera Caslavska.
