Lauren in great shape. Thanks for all of your kind messages.
A source told JustSimonCowell.com: "You couldn't take the smile of Simon's face. Ever since he walked in the hospital he was beaming from ear-to-ear.
"Lauren was so happy to see him when he walked in. It is the perfect Valentine's gift the couple could have."
Despite being two born two weeks early, Lauren and the baby are reported to be in good health.
The couple are naming the baby after the 54-year-old music mogul, according to an attendee to Lauren's baby shower in December.
The source told RadarOnline.com: "It shouldn't come as a shock, but Simon and Lauren really seem to be planning to name their son Simon.
"There were baby clothes and little games all personalised with the name 'Simon' for the baby."
Simon had to miss today's Britain's Got Talent auditions in London today, but sent a message to the show's remaining judges David Walliams, Amanda Holden and Alesha Dixon. It said: "I'm sorry I can't be here today. My son has decided to arrive early. You all have a big responsibility to find some great talent today without me."
- BANG! Showbiz