"Btw a massive, massive thank you to everyone who has sent congrats and well wishes. She's such a beaut. Love you all lots," wrote Peter to his three million followers.
The Mysterious Girl singer, 40, and Emily, 24, have yet to reveal the name of their first child. The couple didn't know the sex of their baby throughout the pregnancy, but have previously said that they like traditional names.
"I like the names Rose, Alexandra and Cleopatra," said Peter.
"Now that I have had the opportunity to tell Junior & Pringles, we are very happy to announce the safe arrival of our beautiful baby girl :)," tweeted Peter, referring to his two children from his previous marriage to Katie Price.
"We are extremely thrilled and mum and bubba are doing fine. We are looking forward to a nice quiet couple of weeks getting to know our baby. Thanks to everyone at the Musgrove Park Hospital :)".