The couple clearly turned to Eva's Cuban heritage when it came to picking their daughter's moniker, as Esmaralda is the Spanish word for "emerald".
Both Ryan, 33, and 40-year-old Eva kept a low profile during her pregnancy and they have not been spotted since the birth.
However they are said to be adapting well to parenthood, and Esmeralda is already Daddy's little princess.
"Ryan is thrilled it's a little girl," a source told Us Weekly last month, adding that the Drive star "hasn't left Eva's side" since they welcomed her into the world.
The hunk's parents and big sister were seen arriving to the couple's Los Feliz home a few days after Esmeralda was born to help out, and they are also said to have a nurse "around the clock".
Meanwhile, an insider told E!: "Ryan is very hands on. Changes diapers, rocks her to sleep-they gave her her first bath together and videotaped the whole thing."
And according to People, Eva is "absolutely in heaven being a mom. She's never been happier. She and Ryan are just in awe of this beautiful person they created. It's a really special time for them."
Eva and Ryan have been dating since September 2011, after meeting on set of their movie The Place Beyond The Pines.
- Daily Mail