The 'Mad Men' actress took to her Twitter account on Saturday to announce that she and her husband James Conran have welcomed a daughter - their first child together - into the world and have named her Ioni James Conran.

She tweeted alongside a photograph of the tiny tot:

James & I are so proud to welcome into the world our healthy and beautiful baby girl, Ioni James Conran! #ioniconran pic.twitter.com/or6c56IiVn

— Coco Rocha (@cocorocha) March 28, 2015
The 26-year-old model is clearly besotted with her new bundle of joy as she's since taken to her social networking site to share a number of adorable snaps of the little one and gush about her.

She wrote:

#IoniConran is growing up so fast. Barely a day old and so alert and expressive! Giving me @GigiHadid vibes here. pic.twitter.com/5d0vadrT5V

— Coco Rocha (@cocorocha) March 29, 2015
And Coco isn't the only one who is keen to share her beautiful baby with the world as her spouse James, whom she married in 2010, has been updating his fans with Ioni's progress.

Alongside a picture of the three of them at hospital, he said:

And then 2 became 3! Coco and I are so excited to be joined by our sweet baby girl, Ioni James Conran. #IoniConran pic.twitter.com/bbPpBkWtfO

— James Conran (@jamesconran) March 28, 2015

There is nothing more surreal and humbling than to look into the face of your baby. #ioniconran pic.twitter.com/dRwrHWGZ2F

— James Conran (@jamesconran) March 29, 2015
James sparked speculation Coco had gone into labour last night after

he shared a photograph of the brunette beauty in hospital.

He captioned it: "#BabyConran has come a long way but her biggest

journey is about to begin."

Irish Canadian supermodel Coco Rocha.Getty Images