Lopez gave birth to twins at 12:45am, according to People magazine.
The actress's representative Simon Fields commented: "Jennifer and Marc are delighted, thrilled and over the moon."
The twins are Lopez's first children and Anthony's third and fourth.
Anthony revealed earlier this month on Latino TV that they were expecting twins. Lopez only confirmed in November that she was pregnant, following months of speculation.
It was reported in January that Lopez was planning to call her twins Max and Emme.