07/09/2008 at 09:00 PM EDT
She may be little, but four-day-old Sunday Rose Kidman Urban has her parents gushing in a big way.
"We feel immensely blessed and grateful to be given this beautiful baby girl," Nicole Kidman
and Keith Urban
said in an exclusive statement to PEOPLE in this week's cover story. "She's an absolute delight."
Kidman, 41, gave birth to Sunday at a Nashville hospital on July 7, with Urban, 40, by her side for the smooth delivery. Also in town to welcome the couple's first child: Kidman's mom Janelle and sister Antonia, who told PEOPLE the new baby is a beautiful addition
to the family.
On Tuesday Kidman's father Antony revealed that Sunday's name
was inspired by Australian arts patron Sunday Reed. Her middle name is a nod to Urban's grandmother Rose.
"Nicole is euphoric," says a friend. "She's wanted this for so long."
For the complete story, including good wishes from country stars Kenny Chesney, LeAnn Rimes, Tim McGraw and others – and the Urbans' domestic routine in their Nashville neighborhood, pick up this week's PEOPLE, on newsstands Friday.