Fallon's wife, producer Nancy Juvonen, gave birth early on Tuesday morning.
"My wife and I thank you for all for the nice baby well wishes. Her first day was the best day of our lives. So happy," Fallon said on Twitter on Wednesday.
The 38-year-old comedian, who is the host of "Late Night with Jimmy Fallon," started out on the long-running "Saturday Night Live" comedy show in 1998.
In April, Fallon was named as the new host of the popular "Tonight" show, which attracts about 3.5 million viewers. Leno was replaced by Conon O'Brien in 2009 but returned to the show a few months later in what turned out to be a public relations mess for NBC.
Along with the change in hosts, NBC said the show will also be moving from Los Angeles to New York.
(Reporting by Patricia Reaney; editing by Mary Milliken and Cynthia Osterman)
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