Jamie Foxx's road to recovery seems to be going very well, 'cause the guy's out and about in public now ... with TMZ getting the first glimpse of him since his hospitalization.

Check out this footage we've obtained, showing a cheerful JF cruising along on a mega-boat on the Chicago River Sunday afternoon ... looking pretty vibrant, and happy to see fans as well. A neighboring vessel passed him by and gave him a big hurrah ... Jamie waved back.

He appeared to be accompanied by a few others onboard as well ... and at first glance, it seems there were some members of his family around. They've been at his side throughout this entire ordeal -- and we know they've been visiting him too as he rehabs in ChiTown.

The difference here ... we're finally getting a clear view of Jamie in the flesh, which is encouraging. Frankly, there's been a lot of speculation about his condition ... and the longer he went out of the public eye, the greater the conjecture would grow. Folks have been worried.

Now, hopefully, all those rumors can be put to rest ... because the guy seems to be well on his way to achieving full health again. Still no word on what exactly happened to him that sent him to the ER in the first place, but the point is -- he seems primed for a comeback.

Here's another positive update TMZ can provide ... we've seen more footage of Jamie spending a night out on the town in the Chicago area Saturday, getting active on his feet, no less, and looking to be in great spirits there too.

That clip is yet an extra sign that the man appears to be doing fairly okay at this point ... and that he's perhaps ready to start venturing out more and more as he gets back to 100%.

Glad to see you, Mr. Foxx. As is the rest of the world, no doubt.