The baby was born at 1:06 a.m. in Los Angeles.
He weighed 7 pounds, 6 ounces.
His name is a tribute to Barker's late father, who died in 2004.
Kardashian and Barker are already parents to daughter Penelope, 9, and son Mason, 12.
They are also stepparents to Barker's 16-year-old daughter, Alabama, and 19-year-old son, Landon.
The couple announced their engagement in October 2021.
They had a lavish wedding ceremony in Italy in May 2022.
Kardashian and Barker have been open about their fertility struggles.
They underwent IVF treatments in an attempt to conceive naturally.
They decided to have a surrogate after they were unsuccessful in conceiving.