We're told Anna's now dating Michael Barrett ... a 47-year-old cinematographer with credits on "Ted," "About Last Night," "Zookeeper," and most recently "Overboard" ... which stars Anna.

There were no signs of romance during production earlier this year, but fast-forward to September when we know they were spending more time together. They were spotted together in Malibu at Neptune's Net, and witnesses tell us they looked very couple-y.

And just this week, they hit up a Pacific Palisades restaurant TWICE, with more reports of PDA.

Chris and Anna fans no doubt remember they met in 2007 on the set of "Take Me Home Tonight."

Anna's new pairing comes 2 months after she and Chris announced their separation. It was clear they were ready to move on when they quickly stopped wearing their rings.