The babies were born early Friday in Long Island, N.Y. The girl was born at 12:12 a.m. and weighed 5 lbs. 7 oz., and the boy followed at 12:23 a.m., weighing 6 lbs.
"Jennifer and Marc are delighted, thrilled and over the moon," Lopez's manager Simon Fields tells PEOPLE exclusively.
They're the first children for Lopez, 38, and the fourth and fifth for Anthony, 39. The couple celebrated the impending births with a baby shower in New York on Jan. 19. "They were just beaming the entire time," said one partygoer.
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Longtime friend Leah Remini calls Lopez "a born mom" and very nurturing. "With our daughter, she's so great. I mean, lets her go in her closet and play with her coats or her jewelry. She's just so giving and loving," Remini said.
Lopez announced her pregnancy Nov. 8, telling the crowd during her final Miami concert: "Marc and I are expecting a baby!" The news of twins was finally confirmed by Lopez's dad earlier this month, in an interview on Spanish-language television.
Lopez Long Kept Pregnancy SecretDuring the early weeks of her pregnancy, Lopez skillfully ducked the question, even when appearing on TV in October with Diane Sawyer and with David Letterman.
Lopez shrugged off the secrecy, telling Harper's Bazaar, "I kind of feel like everybody knew anyway. I was on tour with a bubble gut!"
And being tight lipped has long been Lopez's style. When she married Anthony in June 2004, her rep would neither confirm nor deny the nuptials had taken place.
What are not being kept secret are Lopez's plans now that she's a mother. As she told Harper's, the hard-working performer intends to take time off.
"Once I did the tour," she said, "I really just wanted to shut it down, and since then I've had to do three things, including a video. It may not sound like a lot, but you know, as this point, any woman can sympathize. It is a lot. I was ready just to sit."