"Ryan is madly in love with the baby," an insider told a US publication, adding that Eva, 40, is loving being a mummy.
Ryan Gosling and Eva Mendes are the proud parents of a baby girl
They aren't the only ones infatuated with their little girl; so too are her grandmothers.
"Ryan's mum and Eva's mum have both been helping," the source added. "They have both been great.
"The grandmothers are both very excited and both very hands-on – as much as they can be."
Another insider added to People magazine that Eva is "absolutely in heaven being a mum. She's never been happier.
"She and Ryan are just in awe of this beautiful person they created. It's really a special time for them."
The couple, who met on the set of their film, Place Beyond The Pines, in 2011, shocked fans in July when it was revealed Eva was seven months pregnant.
They were said to be "over the moon" about the prospect of becoming parents.
The photogenic pair have always been discreet about their relationship, but Ryan has been open about his desire to start a family in the past.
"I'd like to be making babies, but I'm not, so I'm making movies," he previously said. "When someone comes along, I don't think I'll be able to do both and I'm fine with that. I'll make movies until I make babies."