The couple's second child, named Henry Lee White, was born Tuesday, a publicist for the White Stripes frontman said Wednesday.
White and Elson have a 15-month-old daughter, Scarlett Teresa White.
"The new child and his mother are both feeling very healthy and happy," White's representative, Chloe Walsh, said in a statement to The Associated Press.
White, 32, married Elson, a 28-year-old model, in 2005. The White Stripes are on a break from their North America tour, which will resume Sept. 13 at the Kiva Auditorium in Albuquerque, N.M.