Wife Barrett delivered son Rhys Edward McIntyre at 9 p.m. Sunday in Los Angeles, the singer's rep confirms to PEOPLE exclusively. "He and his mom are both rock stars," McIntyre, 36, Tweeted on Monday.
Rhys weighed in at 7 lbs., 10 oz.
McIntyre and Barrett, who announced the pregnancy in July, are already parents to elder son Griffin Thomas, 2.
Will the family continue to grow? "I think we have a deal to keep going until we have a girl," laughs McIntyre. "That's what my wife says."
Here We Go Again, McIntyre's latest solo work, is now available on iTunes. On Sunday, the singer will join the New Kids on the Block for a holiday concert in their Boston hometown.
Reporting by MICHELLE TAN