Jay Paxton says Kian Alexander MacKay was born today in Ottawa at 4:52 a.m., weighing eight pounds, two ounces.
The 47-year-old Nova Scotia MP first reported the news on Twitter, thanking people for their prayers and support.
MacKay and Afshin-Jam were married in a private, civil ceremony in January 2012 at an oceanside chapel in Mexico.
Afshin-Jam is a former Miss World Canada who garnered attention in 2003 for her successful campaign to stop the killing of an Iranian girl sentenced to death.
Afshin-Jam was born in Iran, but fled Tehran with her family following the 1979 Islamic revolution and immigrated to North Vancouver, B.C.