Here is the latest (2015.10.15) Aspyr's Steam update for the Sith Lords.
Works on any release with 1.02b update (including GOG).

Installation:
1. Unzip the contents of the archive to the game folder
2. Delete all ATi dll libs from the game folder

If you use any FIGS official localization as base then change
"Language" string in ALI213.ini to the matching one.

Steam version has ~160mb of updated KhoMov0x.bik videos.
So, this patch comes in two different versions:
1. Full - with abovementioned videos (174 mb)
2. Light - without abovementioned videos (14 mb)

Downloads:
Full
Light

THANK YOU!

Incredible!

This patch works perfectly with my copy of the game with Wine and Linux.
No need for a widescreen patch.

In fact, Framebuffer Effects and Grass seem to work now under Wine too, which was not the case before.

I just hope Aspyr will release their work for GOG.com officially in the future, this is too good to be missed.

They said they will. Guess that's about the Mac ports. The patch is supposed to be coming as well.

Is it just me, or is there an odd glitch with this patch where the music becomes inaudible when dialogue plays. It's just dialogue, regular sound effects don't cause this to happen. It's also only present with the new patch.

Nope, it's there.
Also fog effects on Dxun and M4-78EP break.

Not my fault, fellas. I've just packed all changed files from the new release with steam passthrough wrapper.

You can buy this game on Steam and complain to Aspyr about release quality.

Does this patch add the controller support too?

EDIT: Controller support confirmed.

Neat, it actually works! Is there a version of this for KOTR 1 floating around somewhere on the Internet?

Probably not. Aspyr has only updated KotoR II so far, and have not said a word about updating the first one.

But you might be interested in a project called Apeiron.

This is incredible. After trying everything else I was about to give up, but using this patch the game actually starts and works!

Otherwise there was no chance using an Intel HD 3000 and WINE.

This thread should be pinned.

Seconded.

I don't know anything about Steam and therefore this might be too much to ask, but would it be possible to package the entire Linux specific data so someone (like me, ha) could install it over the GOG game data and play native on Linux?

At this point I don't think the patch will ever reach GOG, so help in that regard would be great.

I'm not gonna update this release with the Linux binaries because this would be a plain ass piracy.
Windows version on Steam is just an update over existing codebase, but Linux version is a straight decent port.
You've bought only the original Windows version on GOG, you knew it. Deal with it.

It's only 9,99€ now and you can wait for the summer sale with even more affordable price tag.
store.steampowered.com/app/208580

Fair enough. I don't think the difference between the patch and the binaries is that big, ethically, but it is of course your call. :)
I won't use Steam and its DRM under any circumstances, so I'll continue to wait for the patch to arrive here.