"She is so excited for this next chapter and can't wait to see what the future holds for her and her family," the source continued of Kylie.
Kylie and Travis had already decided on their baby's name long before the reality TV star went into labor, TMZ reported.
According to multiple sources, a Kardashian sister gifted Kylie in late January with a customized, light gray, baby alpaca blanket that had "Stormi" embroidered on it in black, block lettering.
Kylie's family also reportedly gave her expensive diaper bags, a black and white stroller, and a $1,000 white rocking sheep made from real sheepskin.
Kylie kept her entire pregnancy under wraps although months of rumors circulated.
Kylie shocked fans with the announcement of her baby's arrival last week by posting an apology on Instagram for keeping everything a secret, along with an 11-minute YouTube video documenting the last nine months of the new mom's life, including her physical changes and intimate moments with Travis.
Kylie and Travis began dating in April 2017, seemingly only days after she split from her longtime on-again, off-again boyfriend Tyga.
Kylie's romance reportedly became serious in June of last year, and then Kylie and Travis began telling their friends about the pregnancy in early September 2017.
The Jenner and Kardashian clans have had a lot to celebrate recently!