I know this is a really old thread but that's how I managed to fix that, writing that down here since it is the most relevant thread that appears on Google and probably I will run on that problem again.
This applies to VPS solutions since you need ssh and root access to your server.
Greengeeks doesn't come with ImageMagick installed, once you are logged in as root you can verify it by checking that /usr/bin/convert does not exists at all.
First you need to install ImageMagick and all its dependencies using Yum, donwloading the binaries or the RPM package from the ImageMagick website does not work at all.
sudo yum install ImageMagick
Do all the confirmations that Yum asks to you with Y.
Once installed you need to move the ImageMagick binaries on your hosting directory since Greengeeks domains looks like they have open_basedir restriction enabled (cannot access system directories from the website)
On server console:
for i in animate compare composite conjure convert display identify import mogrify montage; do cp /usr/bin/$i ./; done
This copies ImageMagick binaries to your local bin directory at the root of the website.
Replace accountusername with the actual account username of the domain you have created through WHM, generally it is the domain shortened to 8 characters (www.mysitedomain.com => mysitedo)
Then go on Drupal's settings and put /www/bin/convert as ImageMagick path.