Jetpack Photon is free, quick and easy
Image optimization is one of those things you really shouldn’t have to think about. The best way to not think about it is to use Jetpack Photon. With Photon enabled all of your images will be served optimized for free from WordPress’ servers. With Jetpack active and linked, it’s literally a one click process.
EWWW Image Optimizer for the geeks
If serving optimized images isn’t enough, check out EWWW Image Optimizer plugin. With EWWW you can scan your website directories for images and optimize and replace all images. Unlike Jetpack, this will actually save you some storage space. The optimization process is a resource intensive and will slow down your web server. Instead of running EWWW directly, for a small fee you can use EWWW Image Optimizer Cloud which will send all your images to EWWW for processing and then fetch them back.