The 41-year-old socialite took to social media to share a picture of her clutching onto her baby boy's hand.
She wrote on Instagram: "You are already loved beyond words."
Hilton, 41, also admitted she and Reum, also 41, are "exploding with love" for their newborn.
She told “PEOPLE” magazine: "It's always been my dream to be a mother and I'm so happy that Carter and I found each other.
"We are so excited to start our family together and our hearts are exploding with love for our baby boy."
The publication confirmed Hilton had welcomed her baby boy via surrogate.
In December, Hilton admitted she and Carter – who married in November 2021 – had started the IVF (in-vitro fertilisation) process during the coronavirus pandemic.
She said: "We started going and doing it like a few months in because the world was shut down.
"We knew we wanted to start a family, and I was like, 'This is perfect timing. Usually, I'm on a plane 250 days out of the year, and let's just get all of the eggs stocked and ready,' and we have tons of them just waiting."
The star also admitted she and Reum wanted to "enjoy" their first year of married life before "bringing kids into the mix".
She said: "We really wanted to enjoy our first year of marriage together as a couple, you know, before bringing kids into the mix.
"So now that we just had our year anniversary, I can't wait for 2023."
The couple also welcomed another addition to their family in December, when she adopted a new Bengal kitten, named Cutesie.
She shared a video of her spending time with her new feline friend, saying: "Hi, beautiful."
The footage was captioned: "Meet Cutesie Hilton. The newest member of the @hiltonpets family."