Biles, 19, who has won 10 World Championship medals since 2013, scored 62.198 to win her second Olympic medal by a margin of more than two points.
Compatriot Alexandra Raisman got silver with Russia’s Aliya Mustafina third.
Great Britain’s Ellie Downie came 13th, narrowly missing out on becoming the best performing female British gymnast in an Olympic all-around final.
Biles lives up to billing
Biles, described by many as the greatest ever gymnast, had arrived in Rio as the overwhelming favourite for gold and the 4ft 9in athlete delivered in a big way.
Having already led the United States to victory in the team event, she turned the spotlight on her individual brilliance with a dazzling display of power, agility and gravity-defying moves.
She went ahead after the first of four disciplines with a score of 15.866 on vault, although she dropped back to second with 14.966 on the uneven bars, with Mustafina taking the lead at the halfway point.
Biles then turned on the style with an acrobatic beam routine that included a stunning spin to score 15.433 before a floor routine to samba music packed with energetic tumbles, including the move that bears her name.
She scored 15.933 for that final routine and burst into tears when the victory was confirmed.
The United States have now won this event four times in a row, following victories by Carly Patterson in 2004, Nastia Liukin in 2008 and Gabrielle Douglas in 2012.
Biles has more chances for success in Rio as she is also in the vault final on Sunday, the beam final on Monday and the floor final on Tuesday.
Downie misses out on British record
Britain’s Max Whitlock had won a bronze medal in the men’s event on Wednesday, but Downie’s medal hopes ended with a poor score on her third apparatus, the uneven bars, before she made another error on beam.
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Those mistakes saw her drop down from seventh to 13th, to miss out on emulating her sister Becky Downie, who came 12th in the all-around final at the 2008 Olympics in Beijing.
Seventeen-year-old Ellie Downie, the winner of the BBC Young Sports Personality of the Year award in 2015, gained a total of 56.883 after scores of 14.300 on floor, 15.100 on vault, 13.783 on uneven bars and 13.700 on beam.
‘No-one thinks they can beat Simone’
Gold medallist Simone Biles said: “I’m very excited and relieved, I’ve finally done it. You never know the feeling until it hits you.
“I’m not the next Usain Bolt or Michael Phelps, I’m the first Simone Biles. To me I’m just the same Simone.”
Silver-medallist Alexandra Raisman added: “No-one goes into this thinking they can beat Simone.
“I’m sure most people don’t go into it thinking they can beat Usain Bolt, so it’s kind of the same thing.
“We are like sisters. I told her before today, I want you to win and I want second.”
Great Britain’s Ellie Downie said: “I was really happy with how floor and vault went. On bars I lost a bit of concentration, which is something I’ll learn from.
“On beam I didn’t feel nervous and the actual routine was really good but the landing I needed to focus more.
“It’s mixed emotions knowing if I had gone clean I had a chance of a medal, which shows I’m right up there. That’s a big positive to take out of these Games.
“It’s been a bit of a rollercoaster experience but I’m very proud of what I’ve achieved.”