A source previously revealed the former Glee star, 28, had a "very easy birth."
The insider added:: "They are so excited to be first-time parents.
"Naya was born to be a mother and is doing really great so far. And Ryan has amazing paternal instincts and has been waiting on them both hand and foot."
Naya announced she and Justified star Ryan, 32, were expecting a baby in April via Instagram.
Alongside old pictures of them both as children, she wrote: "Surprise! We're having a baby! Ryan and I feel so blessed and can't wait to welcome the newest member of our family."
The brunette beauty celebrated her baby shower with Ryan and friends, including Heather Morris and Amber Riley, in August.
Katherine Jenkins and Andrew Levitas
Katherine Jenkins has given birth to a baby girl.
The 35-year-old opera singer and her handsome husband Andrew Levitas have welcomed their first child into the world and have named the little one Aaliyah Reign.
Taking to Instagram, she uploaded a snap of the tiny tot's hands and feet along with the caption: "Introducing our daughter Aaliyah Reign Levitas, who came loudly into the world weighing almost 7lbs and surrounded by love."
She added: "We are absolutely besotted with her & grateful for the beautiful blessing of this happy, healthy, little miracle. Cwtches all round (sic)."
The blonde beauty announced she was expecting a little girl earlier this year by posting a snap of a pair of tiny pink shoes balanced on one of her wedding pictures on Instagram.
She later added in a statement: "We are overjoyed to be expecting our first child in the autumn.
"Starting a family and moving into this exciting phase of our lives is a blessing for which we are incredibly grateful. We eagerly await the arrival of our little girl!"
Katherine and Andrew married last September and she admitted shortly afterwards she "couldn't wait" to start a family with the American director.
She said: "I can't wait to have kids. I can't wait for us to become a family if and when - God willing - that happens."
Elisabetta Canalis and Brian Perri
Elisabetta Canalis has given birth to a baby girl.
The 36-year-old beauty - who previously dated George Clooney for two years until 2011 - welcomed her first child into the world with her husband Brian Perri yesterday in Los Angeles and has named her Skyler Eva.
The Italian actress took to her Instagram account to announced the news as she shared a photograph of her beau planting a tender kiss on their new bundle of joy.
She accompanied the sweet snap with the caption: "My life is full of love because of you. La mia vita e' piena di amore grazie a voi. Benvenuta al mondo Skyler Eva ! Welcome into the world our lil Skyler Eva 29 - 9 - 2015 (sic)."
Elisabetta announced via a video clip earlier this year she and her husband were expecting their first child after she tragically suffered a miscarriage in June 2014.
Donning a false pregnancy stomach, she said: "I am so happy to share this moment with all of you. Last year you were so cute and you gave me a lot of love. Thanks.
"Now I don't know how to say it. I'm expecting a baby girl! I hope that everything will be fine. Thanks for everything. Thanks for being always so close."
After suffering her miscarriage last year, Elisabetta insisted she still had "hope" of having a family one day in the future.
Elisabetta - who was previously engaged to soccer player Christian Vieri and dated director Gabriele Muccino and 'Jackass' star Steve-O - and Brian live in Los Angeles and got married in Alghero, Italy in September 2014.
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