The actor showed up Saturday night to the Children of Armenia Fund Gala in NYC, and he had Caitlin hanging off his arm as his date. There've been sightings and rumblings of them having already been together of late ... so, it seems they were ready to reveal their romance.

Joe was looking sharp with a traditional suit ... COC was draped in a beautiful green gown. They held on to each other as people fired off photos, and smiled happily for the cameras.

If you're wondering why they were even there in the first place ... it's cause JM was honored with the COAF Humanitarian Award. Sounds like he's been involved with them for a while.

Now, as far as who Caitlin is ... well, she's an actress too -- and like we told you, she met Joe at a 'Winning Time' after-party earlier this year, and they hit it off. She was only in 2 episodes of the hit HBO series, but she's been in a bunch of other stuff as well.

Like we said ... this would be Joe's first relationship post-Sofia ... to whom he was married for 7 years before filing to end their marriage in court earlier this summer. That divorce case is still pending at the moment, but it looks like it might be finalized in due time.

Sofia, meanwhile, is already dating a new fella too ... a respected orthopedic surgeon named Justin Saliman, who's been seen hitting the town with her a lot over the past few months.

Her and Joe's split came out of nowhere this year, but we've heard they'd grown apart ... and that another big reason for their divorce was over kids. He wants 'em, she doesn't.