Giuliana and Bill Rancic Introduce Their Son Edward Duke

(Yahoo!) - Giuliana and Bill Rancic waited a long time for their first child, so they are reveling in new parenthood. Just two weeks after Edward Duke Rancic was born, the proud parents are showing off their miracle baby.

After a gestational carrier gave birth to their 7 pound, 4 ounce bundle of love on August 29, the proud parents immediately bonded with their baby. "I was sobbing and yet had the biggest smile," Giuliana, 37, tells Life & Style in its new issue. "It was very emotional. I just kept saying, Hes so cute." Bill, 41, says Duke (the baby will be known by his middle name) gets his looks from his mother. "The babys got Giulianas dimples," the proud dad gushes. "Every day hes changing — its just remarkable to see. Hes a very cool customer, one happy little guy."

So what is the inspiration behind that happy little guys name? "Edward Duke was pretty much picked out when he was conceived," Giuliana tells the magazine. "Edward is Bills late dads name and my dads name. It was a way to honor them. And Duke means leader."

The Rancics are so happy to be parents that they are even enjoying the less fun tasks of parenthood, including diaper duty and waking up for late-night feedings. "Id never changed more than a diaper or two in my life," Giuliana tells Life & Style. "Now its like the little things that make me happy — happier than Ive ever been." As for those feedings, "we alternate," she explains. "I dont need much sleep, so Bill will do the 8 p.m. before-bed feeding, and Ill do the 12 a.m. and typically the 4 a.m. — though he did do the 4 a.m. last night. Bill just jumped out of bed and was like, Ill do it!"