Unicode Composition in Sublime Text

I just ran into this same issue and I couldn't find an answer anywhere, but I did find a solution. The problem is that the default key bindings in Sublime for Linux overwrite ctrl+shift+u with a soft_redo command. To disable this:

1. Open up your default key bindings: Preferences > Key Bindings - Default
2. Search for ctrl+shift+u and comment out the line containing that key binding. For example: //{ "keys": ["ctrl+shift+u"], "command": "soft_redo" },. Optionally, you could remap this to a different key binding if you really want soft_redo (I have no idea what this command does See comment below for soft_redo functionality).
3. Save and you're good to go!

One note though, you'll need to use <space> instead of <enter> when you've completed the unicode character code as Sublime has a key binding for <enter>.

Edit:

Since you can no longer easily edit the default key bindings in Sublime Text 3, I would suggest using the answer by @brandon-lockaby.

I also got here, but these days it seems you really aren't meant to edit the default settings, and the binding can't be unbound in user settings.

My solution is to press ctrl+alt+shift+u in sublime. It works and I don't have to change any key bindings. Still have to press space when you're done.

By Editing 'Default (Linux).keymap' in /opt/sublime_text/Packages/Default.sublime-package one could disable the conflicting ctrl+shift+u binding

Being a Vim user, I'm used to working with my keyboard, and while my IDE is heavily configured, I like to use default options for computers which are not mine, for instance. This should work.

A possible solution which should work on any default setup:

Type any letter or word (just a placeholder), and just hit Ctrl+D. It selects the word.

Then press Ctrl+H. It opens search and replace. Hit Tab, type \x{<unicode>}, making sure RegEx is activated (toggled with Alt+R), and hit Ctrl+Shift+H to replace it with the Unicode value.

Hit Esc to close the search and replace menu.

If you need the same Unicode several times

After you've done one replacement, you can repeat the same process by selecting (with Ctrl+D again) whatever you want, and Ctrl+Shift+H will automatically replace it, since it stores your last replacement in memory. No need to bring up the menu again.

TL;DR:

Use search and replace. \x{<unicode} in RegEx mode will serve as Unicode characters.