McNearney gave birth to baby Jane on Thursday.
"Congratulations to my beautiful and very tough wife @mollymcnearney on delivering our baby girl this morning," the late-night host tweeted. "Thanks for all your kind baby wishes - turns out, not ALL tweets are mean!" he said in reference to his Celebrities Read Mean Tweets segment on Jimmy Kimmel Live!.
"Kids, don't do drugs. Until you have a baby," McNearney joked later on Twitter. "Then do ALL OF THEM."
A representative tells E! News that "Molly is doing great." Jane is the couple's first child together; Kimmel has two other children from his previous marriage. He and McNearney celebrate their first wedding anniversary on Sunday.