Their new daughter was born on Friday 12 September, according to multiple reports in the US.
The couple announced their pregnancy in July and surprised fans around the world by revealing that Eva was seven months pregnant.
The new parents who keep their relationship out of the limelight, were said to be "over the moon" about becoming parents.
"They literally could not be more excited," a source said at the time.
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.
"Their lives completely changed as soon as Eva got pregnant," the source added. "They used to travel all over the place together and go on hikes with their dogs.
HOW RYAN GOSLING AND EVA MENDES KEPT THEIR PREGNANCY A SECRET
"Ryan has been taking care of her, picking up food and running errands. He has been very supportive about keeping things a secret."
It was only last March that Eva spoke for the first time about her other half, calling him "the best".
Talking about their second collaboration, Lost River, which was Ryan's directorial debut, Eva said: "(Ryan) really created the most beautiful, collaborative, creative atmosphere on set. I know I'm biased. He's the best, he's the best."