Scarlett Teresa was born Tuesday in Tennessee, the Detroit Free Press reported.
The baby was named after "Gone with the Wind" heroine Scarlett O'Hara and keeps with the White Stripes' red color theme, the newspaper said. Teresa is the name of White's mother.
The couple wed June 1 in Brazil with White's ex-wife and bandmate, Meg White, as maid of honor.
Elson is a high-end fashion model who was featured in the White Stripe's "Blue Orchid" video.