Giuliana and Bill Rancic introduce their son, Edward Duke

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, 'He's so cute.'" Bill, 41, says Duke (the baby will be known by his middle name) gets his looks from his mother. "The baby's got Giuliana's dimples," the proud dad gushes. "Every day he's changing — it's just remarkable to see. He's a very cool customer, one happy little guy."

[Related: Giuliana and Bill detail their touching first moments with baby Edward Duke]

So what is the inspiration behind that happy little guy's name? "Edward Duke was pretty much picked out when he was conceived," Giuliana tells the magazine. "Edward is Bill's late dad's name and my dad's 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. "I'd never changed more than a diaper or two in my life," Giuliana tells Life & Style. "Now it's like the little things that make me happy — happier than I've ever been." As for those feedings, "we alternate," she explains. "I don't need much sleep, so Bill will do the 8 p.m. before-bed feeding, and I'll 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, 'I'll do it!'"

The couple, who recently celebrated their fifth wedding anniversary, had a long road to parenthood. On their Style Network reality series, "Giuliana and Bill," they openly shared their struggle to conceive. While Giuliana was being treated by a fertility specialist that the doctor insisted that she have a mammogram, which revealed that she had breast cancer. She immediately underwent a double mastectomy last fall. Because she is taking an oral medication for the cancer over the next four-and-a-half years, Giuliana was told she could no longer try to conceive. So the couple took embryos they had stored prior to the cancer diagnosis and tried their luck with a gestational carrier, who immediately became pregnant.

[Related: Giuliana & Bill Rancic head home to Chicago with 'dream' baby Edward Duke]

Giuliana, who is on maternity leave from "E! News" and "Fashion Police" until November 13 (though she will be covering the Emmys on September 23), says they are so happy with the surrogate process, they plan to do it again. "There will definitely be more kids in our future," she tells Life & Style. "Nothing too soon though. … We'd have to go down the surrogate path again. We got so lucky this first time around, we just hope that we can be so lucky again. We'll see."

For Giuliana and Bill's full interview — as well as loads of photos of baby Duke — pick up the September 24 issue of Life & Style, on newsstands now.

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