Mendes, 40, gave birth to a girl on Friday, according to Us Weekly.
The actress was previously rumoured to have been seven months into her pregnancy back in July when news first broke that she was expecting a child with Gosling.
The 33-year-old actor - who met Eva on the set of their movie Place Beyond The Pines in 2011- has always been open about his desire to start a family.
He previously said: 'I'd like to be making babies but I'm not, so I'm making movies.
'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.'
'Their lives completely changed as soon as Eva got pregnant,' a source previously told People. 'They used to travel all over the place together and go on hikes with their dogs. [But in the past few months] she barely left the house.'
Back in February, Eva denied that she was pregnant following an alleged incident at the Los Angeles International Airport.
Arriving at the Transportation Security Administration point for a routine pre-flight security check, she is understood to have told officers she would not be able to pass through the body scanner 'because she's pregnant', which she later vehemently denied.
A representative for the actress told MailOnline at the time: 'She has never gone through the scanners at the airport, she has always elected to be hand checked instead.'
She later laughed off the baby talk in an interview with Ellen DeGeneres.
'It's so ridiculous,' she said at the time. 'It all started because I didn't want to go through the scanners at the airport.
'You know those X-ray scanners, which are really creepy? They basically see you naked, right? And not only that, but there's a radiation aspect to it, so I always opt out.'
Meanwhile, People report that the pair are now house-hunting for a home for their 'growing brood' and currently reside in a modest two bedroom base in Studio City.
Before Mendes, Ryan was dating his Notebook co-star Rachel McAdams. He also was linked to his Murder By Numbers co-star Sandra Bullock from 2001 to 2002.
Eva was serious with musician George Augusto for nine years. She was also linked to Jason Sudeikis before she met Gosling.