This tutorial was made using The GIMP version 2.8.8
Before you begin making any changes to your original image, make sure to right click on the layer and duplicate it, then click the eye symbol to hide it. That way you have a backup which you can easily revert to if any of the steps go wrong.
The demo image I have used in this tutorial was provided by: haloocyn of www.freeimages.com
Right click on your working layer, then choose “Add Alpha Channel”
To remove the white background, click “Colors” in the editing box menu, then “Color to Alpha”. You will notice that white is the default color. Keep it as it is and click “Ok”. Now your logo image will be on a transparent background, this is visible in GIMP as a grey checkered background.
The image I started with was colored, and now I want to make it a solid black image to use as a logo. To do this I choose “Colors” from the editing box menu again, and then “Colorify”. The default here is also white, but in my case I would like to choose black from the color picker. Click “Ok”.
Now you have a black logo on a transparent background. You may want to check what the logo looks like on a solid white background, to do that simply add a new white layer below the logo layer. If the original image had gradients in it like mine did some parts may be semi transparent. If you do not want the logo to look this way fix it by simply duplicating the logo layer a few times and then merging the layers into one layer (right click on the duplicated layer, then choose “Merge Down”)
Now you can save the logo as a .png file to keep the transparency, for example for web use. You can also use the .gif format for a smaller file size. Note that .png files are better for displaying images with complicated patterns and many colors, .gif files are heavily compressed and you may lose some of the details from the original. Whatever you do, do not save your image as a .jpg file since the .jpg format does not support transparent images and you will end up with a white background anyway. It might also be good to save a version in the GIMP .xcf format so you can return to the original and make changes later if you want to.
Congratulations, you are done!
Part 6 (Optional)
Alternatively, if you would rather have a logo which is solid white or another lighter color to use on a dark background choose “Colors” from the menu and then “Value Invert” to switch the black logo to white. From here you can then colorize the logo further (Colors->Colorify) with whatever color you would like.