The Liberal leader announced the birth of "little Hadrian" on Twitter.
The baby boy was born this morning, weighing in at 8 lbs., 3 oz.
The birth happens to coincide with the 30th anniversary of Pierre Trudeau's famous walk in the snow.
Trudeau's late father took a long walk in the snow on Feb. 28, 1984, to contemplate his future; he announced his resignation as prime minister the next day.
Trudeau says his children, Xavier and Ella-Grace, "couldn't be prouder" to have a baby brother.
He tweeted a photo of the baby's tiny hand, clutching an adult finger.
"Welcome to the world, little Hadrian," Trudeau tweeted.
"8lb. 3 oz. Sophie is wonderful. Xavier and Ella-Grace couldn't be prouder."
Congratulations poured in on Twitter, including from Prime Minister Stephen Harper, NDP Leader Tom Mulcair and Green Leader Elizabeth May.
"@LaureenHarper and I would like to congratulate @JustinTrudeau and Sophie on the birth of their new son Hadrian," the prime minister tweeted.
Mulcair tweeted: "Wishing you all health and happiness."
Earlier this week Trudeau said he'd take some time off from the political arena after the birth.
"I will be taking some time at home with the family, but anyone who has had a newborn in their home knows that it's not time off. It's very much time that is spent focusing on one of the most important things in the universe."Suggest a correction