His representative confirmed the arrival of the baby but without revealing the gender. According to Us Weekly, it is a boy.
Sibi showed off a noticeable baby bump in March when she was supporting Bale at the 86th Academy Awards in LA.
The Dark Knight Rises star, 40, and Sibi tied the knot in January 2000. They are already parents to a 9-year-old daughter, whom they welcomed in March 2005.