2013-12-01: GraphicsMagick 1.3.19 have incorporated this WebP patch ChangeLog-2013
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First, you need Build & Install libwebp
wget 'https://webp.googlecode.com/files/libwebp-0.4.0.tar.gz'
tar -xzvf libwebp-0.4.0.tar.gz
cd libwebp-0.4.0
./configure
make
make install
Then, apply a WebP patch for GM
cp graphicsmagick-webp-patch/patch/gm-1.3.18-webp.patch /opt/GraphicsMagick-1.3.18/
cd /opt/GraphicsMagick-1.3.18/
patch -p1 < gm-1.3.18-webp.patch
Now, you can Build & Install GM just like before
./configure --enable-shared
make
make install
WEBP --with-webp=yes yes
gm convert foo.jpg bar.webp
gm identify bar.webp
Copyright (C) 2003, 2013 GraphicsMagick Group
Copyright (C) 2002 ImageMagick Studio
Copyright 1991-1999 E. I. du Pont de Nemours and Company
This program is covered by multiple licenses, which are described in
Copyright.txt. You should have received a copy of Copyright.txt with this
package; otherwise see http://www.graphicsmagick.org/www/Copyright.html.