The pair have named their daughter Esmerelda Amada Gosling, according to TMZ, which acquired the baby's birth certificate.
The couple welcomed little Esmerelda in Santa Monica on 12 September.
The name Esmerelda is famously the gypsy girl's name in Victor Hugo's 1831 novel The Hunchback of Notre Dame, which was later turned into a Disney hit.
It could be a nod to Eva's Cuban heritage as Esmerelda is the Spanish word for 'emerald'.
And Amada? It's the name of the character Eva herself played in the 2007 movie We Own The Night, and means 'beloved' in Spanish, reports the Daily Mail.
And, if we didn't love Ryan enough already (he's pretty hot, right?), there's another reason to love him even more - he's reportedly a seriously cute doting hands-on dad.
A source told E! News: "Ryan is very hands on. Changes diapers, rocks her to sleep - they gave her her first bath together and videotaped the whole thing."
Another source told People magazine that "Ryan is madly in love with the baby" and that Mendes is "absolutely in heaven being a mum", adding that 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."
We've got more pics of the stunning Eva Mendes right here for you to flick through...
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