The new mum also posted his birth announcement, revealing he arrived on Monday 14 October at 9.54 pm.
"With love we welcome our son, Joseph Frederick Kushner," she tweeted.
Baby Joseph was named after his parents' paternal grandfathers, who the new mum described as "master builders of their generation and inspiring patriarchs of their families."
"Jared's father, Joseph, was a rock. His indomitable spirit, his sense of family, and his work ethic are the values we hope to hand down to our son," she wrote.
"My grandfather, Frederick, was a builder not just of tens of thousands of homes throughout this city, but of a tight knit family that honours to this day the traditions he established.
"Both men set the standards that have been passed down through the generations and which we hope to impart upon Joseph and Arabella. They created a legacy for our family that inspires our careers as well as our love and respect for one another.
"We are honoured to name our son after these two distinguished men. We feel so blessed with the newest member of the family!"
Particularly excited about Joseph's arrival was his big sister Arabella.
Hours after the baby was born, Ivanka shared an adorable picture of Arabella at home with her grandmother "practicing her swaddle".
Shortly afterwards, she was taken by her dad to meet her baby brother at the hospital for the first time, and proud Ivanka posted another photo showing the delighted two-year-old cuddling the tiny newborn.
Ivanka's father Donald Trump has also been celebrating the arrival of his new grandchild.
"My beautiful daughter Ivanka just had a healthy baby boy. Jared and Ivanka are very proud," The Apprentice boss announced. He later added, "Thanks to all for the wonderful congratulations sent to me on the birth of Ivanka's little boy — so nice!"