Source: Kylie Jenner 'Relieved' and 'Overcome With Joy' to Welcome Baby Girl

Kylie Jenner tried to keep her pregnancy private over the last several months, but with constant media speculation it wasn't easy staying out of the spotlight.

So it's no surprise that after announcing Sunday she had given birth to her and boyfriend rapper Travis Scott's first daughter on Feb. 1, the Keeping Up with the Kardashians cast member, 20, is feeling a little relief.

"After the baby was born, Kylie was relieved that the moment was finally here," a source told PEOPLE soon after the announcement.

And even though the delivery room was "a bit chaotic with all the family and friends around," the source added that the Jenner "was overwhelmed in a good way — overwhelmed with the joy, love and support everyone was giving to her and Travis."

The little girl, whose name has yet to be revealed, weighed in at 8 lbs., 9 oz., and arrived at 4:43 p.m., according to Jenner.

The Life of Kylie cast member also addressed the secrecy surrounding her pregnancy while announcing the birth of her daughter, apologizing for not bringing fans along on the journey with her.

"I'm sorry for keeping you in the dark through all the assumptions," she wrote on Instagram. "I understand you're used to me bringing you along on all my journeys. My pregnancy was one I chose not to do in front of the world. I knew for myself I needed to prepare for this role of a lifetime in the most positive, stress free, and healthy way I knew how. There was no gotcha moment, no big paid reveal I had planned. I knew my baby would feel every stress and every emotion so I chose to do it this way for my little life and our happiness."

"Pregnancy has been the most beautiful, empowering, and life changing experience I've had in my entire life and I'm actually going to miss it," she continued. "I appreciate my friends and especially my family for helping me make this special moment as private as we could. My beautiful and healthy baby girl arrived February 1st and I just couldn't wait to share this blessing. I've never felt love and happiness like this I could burst! Thank you for understanding," she added.

To make up for her absence, she also shared an 11-minute video of some of the highlights of her pregnancy, from doctor appointments to intimate moments with Scott and his family.

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