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.