The birth certificate shows the little one has been named Esmerelda Amada, and will take her father's last name.
Amada was the name of Eva's character in the 2007 film We Own The Night.
Their new daughter was born on Friday 12 September at 10.22am, while the announcement came several days later.
The couple revealed their pregnancy in July and surprised fans around the world by revealing that Eva was seven months pregnant.
Ryan, 33, and 40-year-old Eva have always been very discreet about their relationship and are yet to be photographed together this year. The pair met on the set of the 2011 film The Place Beyond The Pines.
Since welcoming their little girl Ryan is said to be completely besotted with his newborn daughter. "Ryan is madly in love with the baby," an insider told a US publication, adding that Eva, 40, is loving being a mummy.
Ryan, 33, shares a close relationship with his mum, having taken her to many red carpet events. He and 40-year-old Eva attended his mother's college graduation together in 2012.
"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."