Travolta's 48-year-old wife, actress Kelly Preston, gave birth to their youngest child Nov. 23. The couple have a 10-year-old daughter, Ella Bleu. Their 16-year-old son, Jett, died in January 2009 after a seizure.
Preston told People magazine she and Travolta had been trying to have another child for three years and were "completely blown away" last year to learn she was pregnant.
"He's given the house a renewed spirit and purpose," Travolta said of his newborn son, who appears on the cover of this week's People with his beaming parents.
The magazine said the "Grease," "Saturday Night Fever" and "Pulp Fiction" star held his wife's hand while she delivered little Benjamin, and Ella Bleu waited outside the room with actress and family friend Kirstie Alley.
Preston's film credits include "Jerry Maguire," "For Love of the Game" and "What a Girl Wants."