The happy couple hit up Via Carota Thursday night and shared a whole lot more than appetizers at the table ... just check out the pics, Gigi's got a pretty firm grasp of Brad's face while they're lip-to-lip and smoochin'.

In fact, the two of them were sorta the picturesque model of lovebirds at an Italian restaurant ... repeatedly kissing not just in front of the cameras but also for all their close friends to see.

So, yeah ... they definitely wanted to show off some PDA here, and on its face -- this feels like them coming out and confirming for everyone, we're an item.

The date didn't end with dinner either, BTW ... BC and GH also strolled around town with Brad walking a dog while Hadid chatted up her close friend Tan France.

Gigi and Bradley's sightings are becoming pretty commonplace ... remember, she hit up Bradley's new cheesesteak food truck in December and grabbed dinner with him and his mom after the Globes in January. With that said, we've never seen them quite like this.

Rumors about the couple first started to swirl in early October -- following her romantic entanglement with Leonardo DiCaprio -- and that only kicked into higher gear when they decided to take a weekend getaway after they were seen out to dinner together.

They've stayed pretty mum on their relationship overall ... but now, these pics from Thursday night seem to be a hard launch of their relationship -- something Brad was reportedly supposed to do at the Oscars, which never happened.