His rep also reportedly confirmed the news to the mag.
However, the source resisted comparisons to fellow late night host David Letterman, whose controversial relationships with staffers have made recent headlines.
"During work hours, they keep things professional," the source said.
Previously, Jimmy and longtime girlfriend, comedian Sarah Silverman, split in 2008, reconnecting in the fall of that year before calling it quits for good in March 2009.
"After Jimmy and Sarah broke up, Molly and Jimmy both found themselves single, and they clicked," the source said. "They're really happy together."
While People reported that Jimmy and Molly have been dating for "several months," it wasn't the first report linking the two.
In July 2008, following Jimmy's initial split with Sarah, the Web site Gawker cited a source claiming the two were dating before sister blog Defamer reported the next day that Molly was still with her boyfriend of three years.
Jimmy went viral in 2008 with "I'm F***ing Ben Affleck," a video response to Sarah's own "I'm F***ing Matt Damon" video.
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