Biles, 17, also won gold in the floor exercise and balance beam in addition to the women's team title.
"I'm glad I'm not competing with her," 2008 Olympic all-around champion Nastia Liukin told reporters before handing Biles the award at a gala dinner in New York marking the 40th anniversary of the organisation founded by Billie Jean King.
Liukin said the powerful, 4ft-9in Biles figured to be hard to beat for 2016 Olympic gold in Rio.
"If she stays on this path, it's very difficult for me to imagine that somebody could come close to where she is."
Biles said she felt honoured to have her name added to a winners' list that included women who had inspired her, including gymnastics champions Gabby Douglas (2012) and Liukin (2008), and swimmer Missy Franklin (2013).
"To be recognised with the award is unbelievable," she said.
In other awards, U.S. ice dancer Meryl Davis was named Sportswoman of the Year in a team sport having partnered with Charlie White to win Olympic gold at Sochi and extend an unbeaten streak through three successive international seasons.
American Noelle Pikus-Pace won the Wilma Rudolph Courage Award for coming back from serious injury and personal setbacks to claim a silver medal in skeleton at the 2014 Olympics.
Kenyan Tegla Loroupe, who after winning three world half-marathon titles and setting two marathon world records has dedicated herself to promoting world peace through sport, received the Billie Jean King Contribution Award.
Using her race prize money, she founded the Tegla Loroupe Peace Foundation in 2003 and has won accolades from the Kenyan government for her efforts.
(Editing by John O'Brien)
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