The pregnant model announced the arrival of her first child via surrogacy on Monday, 19 August, writing on Twitter: "Happiest day of my life. My first son was born this morning."
No further details such as the baby's name have been released yet.
Caprice, 41, announced earlier this year that she and boyfriend Ty Comfort would be expecting two children within weeks of each other as Caprice had discovered she was pregnant after the couple started the surrogacy process.
The model is due to give birth to her second child, another boy, in September.
Happiest day of my life my first son was born this morning xxx— Caprice Bourret (@ByCaprice) August 19, 2013
She said earlier this year: "I've waited 41 years for this, I can't wait! And (boyfriend) Ty is just over the moon and the family, we've had such a great support system."
She added to The Sun: "Words can't describe our happiness when we knew we were expecting two miracle babies."
The businesswoman, who recently joined Lucy Mecklenburgh on a photoshoot, has been open about her hopes of getting pregnant, revealing earlier this year how she'd initially turned to IVF and suffered a miscarriage.
She then spoke with her doctor about "alternatives" and that's why she and Ty began the search for a surrogate. She discovered she was pregnant herself two months after appearing on ITV's Splash.
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