Kerr and Spiegel were initially linked back in June 2015 and got engaged a little over a year later.
"We're just really excited to expand our family", Kerr, 35, said at the time.
The birth of little Hart means that Miranda's first child Flynn - whom she shares with ex Orlando Bloom - now has a little brother to play with. "Thank you for the kind words and wishes during this very special time", they told People magazine in an exclusive statement.
TMZ first reported that the model gave birth to her son on Monday evening in Los Angeles at 11:53 pm.
When Kerr announced her pregnancy a year ago, she didn't actually reveal the gender of her baby.
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Well, the newborn is named after Spiegel's grandfather, who is a powerful attorney in San Francisco.
Miranda announced the news that she was expecting in November, with her spokesperson saying: "Miranda, Evan, and Flynn are looking forward to welcoming the newest member of their family". "I have been getting hormonal headaches, which I never got with Flynn", she said.
Kerr's second pregnancy wasn't an entirely smooth ride.
In May, the former lingerie model married Spiegel in what was described as an intimate celebration in the backyard of his home in Los Angeles.