There is a plugin for the Gimp that provides the ability to load and export WebP images. You can install the package (gimp-webp) from this PPA:

ppa:george-edison55/webp (Click here for instructions on using PPAs.)

The commands for doing this would be:

sudo add-apt-repository ppa:george-edison55/webp

sudo apt-get update

sudo apt-get install gimp-webp

Once the package is installed, open up the Gimp and you will now be able to export images to the WebP format:

The package is currently available for Trusty, Utopic, Vivid, and Wily.

_{Disclaimer: I am the author of the plugin.}