Kim Kardashian's Family Congratulates Her and Kanye West

Update Sunday June 16, 2013 05:00 PM EDT Originally posted Sunday June 16, 2013 03:55 PM EDT

Father's Day came early for Kanye West, who welcomed his first child with girlfriend Kim Kardashian on Saturday morning.

Although PEOPLE confirmed the news through a source, the Kardashian family has remained uncharacteristically mum on social media – until Sunday afternoon, just in time to honor the day for dads.

"HAPPY FATHERS DAY @kanyewest !!!!!" Kardashian matriarch Kris Jenner Tweeted.

Jenner's shout out was followed by a message from Kim's sister, Khloé Kardashian Odom, who Tweeted, "I cannot even begin 2describe the miracle that is now a part of our family. Mommy/baby are healthy & resting. We appreciate all of the love."

In a follow-up Tweet, she addressed the public's curiosity in further details on the infant, explaining with a heart icon, "More info will come when the time is right! Thank you all for understanding! We love you all dearly! Overwhelmed with love right now."

Kim, 32, who appears to have gone into labor several weeks early, was accompanied by her beau, 36, at the hospital when she gave birth to their baby girl, whose name has not yet been released to the public.