Biles, 19, won four gold medals in Rio, five in total, as a member of the Games' best gymnastics team.
"It's an incredible honor to be selected as the flag bearer by my Team USA teammates," Biles said in a statement.
Sunday will mark the second time a gymnast has carried the Stars and Stripes into an opening or closing ceremony. The first was Alfred Jochim in 1936. A silver medalist in 1932, he carried the banner into the opening ceremony at Berlin.
In addition to winning gold in team competition, Biles won the all-around title, floor exercises and vault. He took bronze on the balance beam. Her five medals matched the totals of Nastia Liukin in 2008, Shannon Miller in 1992 and Mary Lou Retton in 1984.
Biles has said would take time to consider whether to continue her gymnastics career with an eye toward the 2020 Tokyo Games.
Sunday's closing ceremony is scheduled to begin at 7 p.m. ET.