"It's been going on for around six weeks," says a source. "They are really happy. They have actually known each other a while through mutual friends and would sometimes bump into one another at industry events, but it has only just turned into something more."
"He is obviously really smart...and Kristin is very intelligent, too," adds the source. "They have a lot to talk about."
The couple, who have both been open about past substance abuse struggles and their subsequent sobriety, have "been out quite a few times on both coasts," according to a source.
The 50-year-old West Wing creator was married to Julia Bingham from 1996 to 2005. He's also been romantically linked to Kristin Chenoweth.
Davis has never been married, and her rep declined to comment on her personal life. Besides the Sex and the City flicks, she recently starred in Journey 2: The Mysterious Island.