"Words cannot explain how happy we are to welcome our beautiful son into our family. Miranda is doing well and Flynn is excited to be a big brother," reps for Kerr and Spiegel shared with People overnight.
"Thank you for the kind words and wishes during this very special time."
They also report that the newborn baby's name, Hart, is a tribute to Spiegel's grandfather.
Kerr and her Snapchat founder husband first announced they were expecting a child together back in November.
“Miranda, Evan and Flynn are looking forward to welcoming the newest member of their family," a spokesperson said in a statement.
The couple, who first announced their engagement in July of 2016, wed in a private ceremony on May 27th 2017.
34-year-old Kerr already has a 7-year-old son Flynn, whom she shares with her ex-husband Orlando Bloom.