The 40-year-old revealed on Tuesday that she and her husband, Snapchat chief executive Evan Spiegel, had decided to name their newborn Pierre.
In a post to Snapchat, she said: "We are overjoyed by the arrival of our little ray of sunshine, Pierre Kerr Spiegel.
"We couldn't be more excited to welcome our fourth son into our family. Feeling so very blessed."
The message sat at the top of an image of some flowers, baby socks and what looked to be a piece of clothing that had the name Pierre embroidered on it.
Kerr had announced her fourth pregnancy in September.
The model gave birth to her first son Flynn in 2011, whom she shares with ex-husband Orlando Bloom.
She was married to the Pirates Of The Caribbean star, who now shares a child with his partner Katy Perry, from 2010 to 2013.
The model tied the knot with Spiegel in May 2017 after announcing their engagement on social media in July 2016.
The couple had started dating in 2015, having first met at a dinner in New York the year before.
In 2018 they welcomed their first child together, a baby boy called Hart, and in 2019 their son Myles was born.
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