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The couple stepped out together for the first time to attend O'Donnell's Rosie's Theater Kids Gala on Monday night in New York City.
A friend of the pair revealed that O'Donnell and Rounds met at Starbucks several months ago.
The source told People: "They are adorable together and are very, very happy."
O'Donnell is a mother of four with her ex-wife Kelli Carpenter and also recently dated Tracy Kachtick-Anders.
The television presenter recently claimed that she was once filled with "rage", but has learned to become a happier person over time.
O'Donnell will host an upcoming talkshow for the Oprah Winfrey Network.
> Rosie O'Donnell wants Russell Brand for first OWN show interview
> Rosie O'Donnell: 'I'm a good fit for Oprah Winfrey's OWN'
Watch a clip from Rosie O'Donnell's recent appearance on Curb Your Enthusiasm below:
