The following is how-to created by my friend Otaku over at Unpleasant Street! 

Tea light hacking instructions:

Parts you'll need:

bullet

Ultrabright LED 1 each  (I used a white LED)

bullet

Diffuser for LED. 

bullet

Small gauge wire

bullet

4AA battery holder (use the flat type, it will be easier to mount to a lantern)

 

Remove the battery tab from the tea light and turn it on to make sure it works.  Use a razor blade or X-acto knife to cut away the silicone "flame" molding.

 

Cut off the original LED leaving as much of the leads as possible exposed.  Solder the new LED to the leads.  Check the polarity before doing this so you only have to do it once.  You can do this by touching the new LED legs to the cut leads and seeing when it lights up.

 

Remove the battery cover and the batteries.  Solder in the small gauge wires as shown.  The red wire is the positive lead.

 

Cut some small notches in the battery cover to accommodate the lead wires and replace the cover. 

Connect the battery leads to the 4AA pack and turn on the light.  If it doesn't come on re-check the polarity of the LED.

 
You'll probably need diffusers as many of the ultrabright LEDs are beam-type and don't spread light very well.  The diffusers pictured on the right came from Michaels for about $2.50 a package. 

Choose the diffuser color you want to use and drill a 5mm (~.200") hole into the bottom.  If you use the diffusers shown in the picture, pull of the little rubber "threaded" cap and cut off the small knob before drilling.  It helps a bit to sand the base flat – it keeps the drill point from skipping around.  Place it on the LED with a bit of glue.

 

Recommendations:

Cover the white plastic shell of the tea light with black tape or paint.  Also do this to the bottom of the LED, if you used a white one.  There is some light leakage through the bottom of the LED that will wash out the colored diffuser a bit.

Click the picture on the right for a video of the finished product

 

On the right is an example of Otaku's tea-light hack with some modifications added by me.  I removed the top, used a 10mm 60,000mcd LED, then hot glued the top onto the LED so just the tip came through.  I trimmed the old flame and hot glued it to the tip of the LED as a diffuser.
To the right is the Otaku tea-light hack for the Funkin and JoAnn LED Tea Light using the 10mm 60,000mcd ultra bright LEDs.  The key for using this hack seems to be that the original uses a single color, single element LED.
LED Tea Light from Globe Light as it comes out of the box.  This video compares the tea light before Otaku's hack below.
LED Tea Light from Global Light with Otaku's Hack reusing the old flame as the diffuser and a 10mm 60,000mcd LED.
Still to come, using PVC and hot glue to turn the 10mm LED hack into something that looks like a candle again.