The Smashing Pumpkins frontman, 48, and 22-year-old artist Mendel, the daughter of fashion designers Gilles Mendel and Jenny Mui, became parents to a son named Augustus Juppiter Corgan on 16 November (15).
Corgan is known for keeping his personal life private, but in 2010 he opened up about his hesitation to have children.
"I've never had any kids," he told Alternative Press. "I think there's some sort of mystical connection in my mind that my father's father didn't claim him and my father didn't claim me. That has everything to do with why I don't have children."
The singer was previously married to art conservationist and artist Chris Fabian from 1993 to 1997 and has also been linked to Courtney Love and Jessica Simpson in the past.