"We are proud to finally give you all a first glance of our little princess Pearl."
Nick has also revealed that the couple were considering calling their older daughter Saoirse, 20 months, Pearl instead.
He told Us Weekly: "Essentially, we kind of gave up on the name, but Lauren really liked Pearl.
"Then we discovered that we were going to have another baby. That's when I was like, 'Listen, let's go with what you wanted.' So she became Pearl."
Pearl's arrival into the world didn't go as planned, as there were "minor complications" at birth.
However, mum and baby got "home safe and sound" and were recovering well after a longer stay in hospital than expected.
In an update, Nick - who also has Odin, 5, with his spouse - tweeted at the time: "Ok everyone, I wanted to let you know that finally, we are home safe and sound.
"Baby is doing so much better. I'm going to share a little picture with you really soon. Thank you again for all your love."
Nick announced the arrival of their third child and promised to let fans known how mum and baby were doing.
He wrote: "We are proud to announce that our baby has officially arrived. But as a parent knows all too very well, sometimes things don't turn out the way you plan it. We have been experiencing some minor complications but things are looking a little better after the first night.
"I wanted to thank everyone for all the prayers and good thoughts during this time. We will keep you updated."
Nick, 41, and Lauren, 38, announced they were expecting back in January, which came after the couple experienced multiple devastating miscarriages as they tried for a third child.
Lauren said: "I was fully set on just having two children and I had prepared for that and made arrangements for that. We were going to have two children and it was a surprise. I didn't find out I was pregnant till I was about five-and-a-half months pregnant. I didn't have any symptoms, I didn't have anything indicating that I was pregnant.
Lauren feared she was seriously ill rather than pregnant and they were considering surrogacy.
"One day I just, I felt something move in my body and I said, 'Nick, there's something not right. I think I need to go to the doctor. Something's wrong with me.' I was not supposed to be able to have any more children, so I never assumed that I was pregnant."
