“After the baby was born, Kylie was relieved that the moment was finally here,” a source tells PEOPLE

By Elizabeth Leonard and Maria Pasquini
February 04, 2018 04:58 PM

Kylie Jenner’s one proud mama!

After months of secrecy, the Keeping Up with the Kardashians star revealed that she had given birth to her and boyfriend Travis Scott‘s first child — a girl — on Thursday. The little girl weighed in at 8 lbs., 9 oz., and arrived at 4:43 p.m. local time.

“After the baby was born, Kylie was relieved that the moment was finally here,” a source tells PEOPLE.

And even though the delivery room was “a bit chaotic with all the family and friends around,” the source adds that the 20-year-old “was overwhelmed in a good way — overwhelmed with the joy, love and support everyone was giving to her and Travis.”

Kylie Jenner’s baby
| Credit: Kylie Jenner/Youtube

Want all the latest pregnancy and birth announcements, plus celebrity mom blogs? Click here to get those and more in the PEOPLE Babies newsletter.

Credit: Kylie Jenner/Youtube

“I’m sorry for keeping you in the dark through all the assumptions,” Jenner wrote to fans as she revealed her baby news 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.”

Continued Jenner, “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 said. “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.”

Alongside her announcement, the lip kit mogul also shared a video montage documenting “the last 9 months,” including a quick shot of her and the baby in the delivery room after her arrival.

“Whatever your name is going to be, this is how I found out about you,” Jenner’s BFF Jordyn Woods said in the video, as she explained how Jenner learned she was pregnant.

“One day, I was in your mom’s bathroom with her and she took a little test,” Woods said.

After Jenner looked at the pregnancy test, “She passed it to me after, like, ‘Surprise.’ She just looked at me weird and I’m like, ‘What?’ And I didn’t know that’s what she was doing so when she passed it to me I was like …” Woods explained, making a shocked face.

Jenner’s assistant Victoria Villarroel also remembered being stunned when Jenner, as Woods said, “gave us a look.”

“I was like, ‘This is a baby!’ ” Jenner’s assistant exclaimed.

Later, Woods discussed her BFF becoming a mom at such a young age:”When you’re 20 years old, you’re just figuring out your life. You don’t know what you want. You’re an indecisive teenager and you’re just becoming a young adult, and there was one thing that your mom knew for sure, and that was you.”