"Happy Birthday to our baby boy Sebastian 'The Bash' Taylor Thomaz! I'm so happy u guys I fell in love all over again," said Amber.
Earlier that day Wiz Khalifa posted a message of himself wearing hospital scrubs with the caption "Daddy time".
"Everyone welcome this perfect young man into the world," he wrote later that day. It appears the Wiz is off to a good start as a father. Rose tweeted a photo of the rapper holding their little boy with the caption, “Best daddy ever…. Up with the baby so Muva [Rose's nickname] can go back to sleep :-).”
Celebrity friends have also been using the social media site to send messages of congratulations to the couple.
Rihanna tweeted a picture of herself and Amber Rose, adding "Congratulations to my fam mistercap and @darealamberrose !!! Welcome baby Bash! You're born in an exquisite month #babypieces".
"Welcome 2 fatherhood mistercap!!! Congrats 2 u n @darealamberrose on ur new son," wrote Snoop Dogg.
Wiz Khalifa, 25, is known for songs including Black and Yellow and his collaboration with Maroon 5 on Payphone.
He and Amber Rose got engaged in 2012. She has previously dated Kanye West and has made cameos in music videos for Nicki Minaj, Ludacris and Young Jeezy.
I'm so happy for the couple. First the engagement now the baby. What a great start for a relationship. Congratulation and good luck to the both of them! :-)