Henry was born Monday in Los Angeles. He weighed 8 1/2 pounds, said Roberts' publicist, Marcy Engelman.
"All of the Moders are doing great," Engelman said in a statement.
Roberts, 39, and her husband, 38-year-old cinematographer Danny Moder, have 2-year-old twins, Hazel and Phinnaeus.
The couple were married in July 2002 at Roberts' home in Taos, N.M.
Roberts won the best actress Oscar in 2001 for "Erin Brockovich." Her screen credits also include "Steel Magnolias" and "Pretty Woman."
Photos: Celebrity Babies
Roberts voiced the wise spider in the 2006 film adaptation of "Charlotte's Web." She'll next be seen in the drama "Charlie Wilson's War," directed by Mike Nichols, which is scheduled for release later this year.
Late last year, in an interview with Diane Sawyer, Roberts, 39, gushed about "having the best family."
"The idea of getting older just, to me, is having more adventure with (my family), and getting to know my kids better, and getting to, you know, intertwine my life with my husband more," she told Sawyer.
A request for comment from Roberts' publicist Marcy Engleman was not returned to The ShowBuzz on Monday.