The Fashion Star host and husband Bill Rancic welcomed the baby boy via gestational surrogate on August 29.
Writing on her Twitter page on Friday, Giuliana shared her happiness at being a first time mother.
"It's true what they say (and what u all told us)," she posted. "@BillRancic and I couldn't love little Duke anymore than we do. He's a dream...."
The couple announced they were expecting the child in April 2012.
Bill has told Digital Spy that Edward will appear in their reality series Giuliana and Bill.