Hargitay, 47, and husband Peter Hermann, 43, adopted Amaya Josephine, who was born a week ago in the United States.
"I'm deliriously happy," the actress says. "From the minute she was born, she was just surprisingly alert and so full of love."
"We were considering both international and domestic adoption and we're thrilled that this is the way our prayers were answered," she adds. "We talked a lot about mixed-race adoptions, and we are very excited that we are now a multi-racial family. We're just so happy she's here."
This is the second child for the couple, who married in 2004. Four-year-old son August is just as excited as his parents.
"He is over the moon," Hargitay says. "He calls her his baby because he says the whole thing was his idea. He always talks about how he's going to protect her. He's going to be a great big brother."